De Greene, Kenyon B., "Equilibrium, Critical Points, and Structural Stability and Change in System Dynamics and Systems Science", 1983

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EQUILIBRIUM, CRITICAL POINTS, AND
STRUCTUAL STABILITY AND CHANGE
IN S¥STEM DYNAMICS AND SYSTEMS SCIENCE

Kenyon B. De Greene?
Institute of Safety and Systems Management
University of Southern California
Los Angeles, CA 90089-0021

ABSTRACT

The need for grand unifying principles of the evolution of
societal systems is stressed. Examples of such principles from
other sciences are given. The economic long-wave or Kondratieff
cycle is taken as a reference basis for the study fo the evolu-
tion of contemporary technological societies. A number of
qualifications to the basic paradigm are made. Several areas of
recent structural stability theory are discussed in terms of
their relevance to societal evolution, Particular stress is
placed on nonequilibrium and bifurcation situations. Structure-
function-behavior interrelationships at and near critical points
are considered the most important features pertinent to system
change or reconfiguration. Attempts are made to provide a fuller
integrated theory of societal evolution and structural change.

A number of problems relative to system dynamics theory and model-
ing, and to the use of models in societal management, are
introduced and suggestions for improvements made.

INTRODUCTION

This paper is a further attempt to develop an integrated field
theory of societal structure and evolution, especially as pertain-
ing to conditions around points of sudden reconfigurational change.
The paper considers issues relevant to the design and use of
large-scale computer simulation models in science and for
policymaking. A number of emergent policy problems dealing with

Management toward the future society are discussed. Previous

pease address correspondence and requests for reprints to 4345
Chaumont Road, Woodland Hills, CA 91364, Tel (213) 340-5199.
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publications, including broader discussions and definitions and
reference to earlier works of this and other authors, are [1],

(2], (31, [4], [5].

That new approaches to theory modeling and management are
vitally needed is evident from the mounting numbers and complexity
of societal problems. Social, technological, and economic
policies and institutions, that have apparently worked for decades,
or longer are now widely perceived as faltering. One gets the
the impression of the imminent collaspe of many policies and
institutions, that have devleoped quite respectable lineages,

followed by a major paradigmatic shift.

Both theoretical and realworld problems, of course, are
those of the interrelationships among structure, funciton, and
behavior and of evolution, stability and instability, and change
in form. Recently, advances in theory, modeling and understanding
of and data collection on realworld systems have greatly improved
our capabilities for dealing with these complex systems on both
theoretical and practical grounds. These advances include
Forresterian system dynamics, new ways of looking at equilibrium
situations, new approaches to describing discontinuous qualitative
changes, and the availability of data on structural change in

managed living systems, particularly ecosystems.

In the following subsection of this section we shall discuss
further the reasons for our optimism about the immediate likeli-~
hood of developing an integrated theory of societal evolution. We

shall also bring up the topic of "aging systems approaches,” whose

properties parallel those of aging technologies, organizational

designs, management strategies, etc.

In the second section of this paper we shall review and
evaluate research on societal long waves. In the third section
we shall discuss different meanings of equilibrium and the role
of equilibrium in structual stability and change. In the fourth
section we shall discuss the existence and nature of critical
points or thresholds beyond which system structure and behavior
bifurcate or otherwise change qualitatively and quantitatively.
In the last section we shall attempt a brief theoretical
synthesis of societal evolution at our particular time in world
history. We shall consider implications of the present structural
instability for planning and policymaking for the management of

society.

On Grand Unifying Principles

Recently there appears to have been a paradigmatic shift
within science. Scientists in many fields are working on the

same kinds of problems, namely, those adumbrated above as
structure~function-behavior interrelationships, stability, change,
and evolution. Increasingly, similarities rather than differences,
are evident in apparently very different living and nonliving
systems. Although the forces of institutional reaction remain
strong, it appears that the decades - long pathological speciali-
zation no longer represents the unquestioned dominant voice of
science. Theory~ and model-building based.on the search for

suggestive analogies and metaphors and the use of general constructs
(building blocks) can be called the constructural approach.

Other, and I believe inherently doomed, attempts to overcome

the artificial barriers set up by disciplinary specialization

are the multidisciplinary (e.g., how do you get sociologists and
engineers to work together in urban design?) and interdisciplinary
(e.g., what are the interfaces or interrelationships between

economics and sociology?) approaches.

The integration of previously separate bodies and knowledge
has been spectacular in several sciences, perhaps most so in
molecular biology, geology, and theoretical physics. I shall

comment briefly only on the last two.

In geology the grand unifying principle is plate tectonics.
Plate tectonics, which was fully formalized in the early 1970s,
integrated major geological concepts that went back more than a
century. Zach concept in turn was underlain by substantive sub-
concepts and by verifying evidence. The major concepts include
continental drift, building of major mountain chains, origin and
distribution of volcanos, origin and distribution of deep ocean
trenches, distribution of mid-ocean ridges, origin and distribu-
tion of earthquakes, shifts in paleomagnetism, and the behavior

of large strike-slip faults like the San Andreas.

Grand unifying principles apply at two levels in theoretical
physics. Since Einstein, attempts have been made to develop a
unified field theory of gravitational, and electromagnetic, weak
nuclear (e.g., in radioactivity), and strong nuclear (e.g., in

quark bonding of protons) forces. A quantum field theory at the

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elementary-particle level now unifies the last three kinds of
interactions [6].

At the atomic and molecular levels scientists have long been
familar with phase shifts, rather dramatic shifts in structure and
behavior on either side of a critical point, typically a critical
temperature. Superficially very different substances, for
example, gas-liquid mixtures, immiscible-liquid mixtures, ferro-
magnets, metal alloys, and solid-state devices display very similar
behaviors. These behaviors are called critical phenomena. The
similarity of qualitative behavior was recognized by Landau in the
1930s and is called mean-field theory. Mean-field theory explained
mean or average behavior, but neglected fluctuations. Recent
theory explains how quite dissimilar appearing substances show
quantitatively exact behavior (i.e., have exactly the same critical
exponents) in the neighborhood of critical points. Identical
behavior is dependent on having the same dimensions of space and
of order parameter (a macrosgopic or emergent property such as

susceptibility to magnetization).

The existence of critical points or regions “near" these
points and of incipiently changing structure and behavior is a

key construct in the theory I am attempting to develop.

I feel far less optimistic about the progress, both
theoretical and applied, made in the last two decades in any of
the traditional behaviorial, social, organizational, and manage~
ment sciences. In spite of "exponential" growth in the numbers

of practitioners, publications, university departments, students,
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and so on, one gets the impression of stagnation in theory-
building, basic research, and applications. such fields as
human factors, operations research, systems analysis, systems
management, public administration, and systems engineering may
have passed their useful performance peaks and may have little
more to offer in terms of needed radically new ideas. Many
systems dynamicists would add econometic modeling to this list!
This problem of the aging of institutions and practices and of
structural bonds is pursued in greater detail throughout this

paper.

one major attempt to develop a grand unifying principle

for social systems — an approach that can powerfully challenge
the intellect and inspire the efforts of others — is that of
Jay W. Forrester. With system dynamics, and especially with the
recent work on the System Dynamics National Model of the socio-
economic system of the U.S. and other developed countries,
insights have emerged that help explain short- and long-range
cyclic behavior and reconcile once apparently contradictory
economic behaviors. These holistic patterns of behavior include,
as relevant to today, simulataneous low productivity, aging
institutions, stagnant economic growth, differential industrial
performance, high unemployment, industrial overcapacity, high
interest rates, recession, inflation, and (I add) increased spe-

culatory behavior. See, for example, [7, 8].

There has been some confusion over the meaning of the term

system dynamics. It can mean the specific theoretical and

modeling approach developed by Forrester. It also has a more
generic meaning referring to the behavior of any dynamic(al)
system. Partly for this reason, and partly to coincide with
systems analysis, systems engineering, systems science, etc., I
have long urged the use of systems dynamics to describe
Forrester's approach. A number of different kinds of "system
dynamicists", including dissipative-structure theorists, met at
the 7th International Conference on System Dynamics held in June

1982 in Brussels. At that time the term classical system dynamics

arose as a description of Forrester's approach. Perhaps
Forresterian system dynamics might also be appropriate. At any
rate, the conference represented one step further toward the
development ofa grand unifying principle for the societal sciences.

See [9] for further discussion of the conference.
SOCIETAL LONG WAVES

A major deficiency of science, outside cosmology, geology,
palentology, and evolutionary biology, has been its emphasis on
cross-sectional ahistorical theories and methods. Even subjects
like history have been fragmented, with overemphasis on great
persons and specific events, and with associated nelect of basic
@riving forces and dynamic behaviors. Recently, many economists,
stimulated largely by today's recurrent crisis and deteriorating
economic situation, have begun to take a much longer-range view
of the processes of economic change. The partially forgotten
work of men like J. van Gelderen, N.K. Kondratieff, J.A. Strumpeter,

and J, Schmookler have been revived, reexamined, and reinterpreted.
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Economists and many modern businesspeople speak increasingly
of economic long waves and Kondratieff cycles, and concern over
the causal factors underlying and means of controlling these
patterns has become an active area of research. For example,
the entire August 1981 issue and most of the October 1981 issue

of Futures was devoted to this topic.

Before analyzing and interpreting some of the crucial points
made by other authors, let us first see how the concept of econo-
mic long waves fits into the theory of societal evolution that I
am trying to develop. Earlier presentations of this theory, that
emphasizes families of logistic (or logistic-like or convex-up
parabolic) curves of social/cultural, demographic, and technolo-
gical change, with these curves sometimes overlapping and sometimes
separated by discontinuities and overall bounded by a hyperbolic

envelope curve, are given in [3] and [4].

Fundamentally, I question the existence of "economic" long
waves, in the sense that the economic factors are the sole or main
contributory, causal, or controllable factors. I question that
cycles or recurrent patterns of rise and fall or growth and
decline are inherent only in the structure of Capitalism or of
the industrialized world since the beginning of the Industrial
Revolution. Rather, I propose that such recurrent patterns are
intrinsic features of human organic and cultural evolution. The

primary concept is that of the sociotechnical system, which also

typically has economic and political dimensions. Indeed, the

primary role of technological change is stressed by many of the

Futures authors, and others emphasize the need for associated

social or institutional innovations (e.g., Forrester [7], [@1).

There is much evidence for alternating continuity and
@iscontinuity in human evolution. Carneiro, for example, (cited
and discussed in [3] and [5]) contrasts periods of development
(i.e., discovery, invention, and innovation) with periods of
growth (diffusion of established technologies and practices), In
Anglo-Saxon England the period of development lasted between 450
and 650 A.D. where it was separated by a discontinuity (change in
slope) from a period of growth that lasted until 1087 A.D. The
second period represented a consolidation and spread of basic

innovations from the first period.

Many analysts identify four long waves since the beginning

of the Industrial Revolution with troughs and peaks for each wave

given as follows: (1) late 1780s/about 1816; (2) 1843/about 1863;
(3) 1896/early 1920s; and (4) late 1930s/late 1960s. A fifth
trough is often predicted to occur near the year 2000. Successive
waves have been associated with different dominant technologies

and nations. The first wave involved mostly Britain and the
technologies of textiles and steam power. The second wave
involved more of western Surope and drew heavily on coal, the
railways and mechanization of production. The third wave involved
also the U.S. and exploited electrical power, the petroleum
industry, the chemical industry, and the internal combustion
engine. The present wave, increasingly worldwide, has been closely

associated with electronics and computers, ariplanes, and further
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advances in the chemical industry such as plastics, pharmaceuti-

cals, and synthetic fibers.

In placing these long waves in the broader context of
long-term evolution, Piatier [10] uses the concept of an indus-
trial revolution. He includes the Neolithic revolution based
on agriculture, animal husbandry, and settled village life with
its spinoff of greater hierarchical or bureaucratic organization

and master and slave relationships.

But why limit concern to such isolated revolutions? why
not provide a sequence of sociotechnical and social revolutions,
each of which might be regarded as a bifurcation point in human
evolution? A detailed presentation of the argument is beyond the
scope of this paper. However, a full understanding of societal

evolution, and an understanding of forces operating near the

present and in the future, would also have to include these repre-
sentative revolutions: (1) the pre-Paleolithic recognition of the
importance of tools and the passing on of the knowledge from one
generation to the next; (2) the pre-Paleolithic or Paleolithic
discovery of the controlled use of fire; (3) the successive Paleo-
lithic refinements in the knapping of flint and other raw materials
used for tools (these successive technologies were, by the way,
one of the bases for the development of hyperbolic-growth theory),
(4) the Mesolithic or Neolithic discoveries of agriculture and

the domestication of animals and the spinoffs mentioned above;

(5) the late Neolithic invention of the wheel; (6) the discovery

of the use of copper, tin, zinc, and iron for weapons and other

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implements; and (7) religious changes, perhaps most importantly
the Protestant Reformation, that led to an excessive drive to
excel, to the familiar "work ethic," and to rapid expansion of
knowledge and trade in some countries while other countries

remained static.

Quite obviously the history just adumbrated shows a tele-
scoping of sociotechnical change. Stages, defined in terms of
the span from first discovery of a new idea or technology through
complete satuation of the cultural environment with the resulting
and diffused innovation, may have lasted hundreds of thousands of
years in the early Paleolithic, several hundreds of years in the
early Middle Ages, and several tens of years recently. Probably
from the very beginning the soéiotechnical system consisted of
a complex of interrelated ideas, beliefs, technologies, and
practices. Such complexes are much larger and have much faster
and greater impacts on the environment today. Recognizing these
complexities and their impacts —that is, recognizing the total
field of forces — should caution us against any monocausal
explanations of societal long waves and against any precipitous
implementation of policies. Consider in [11]:” ....proposal may

provide an alternative to Reagonomics."

Another observation important to the building of the unified
theory and to systems science is the ubiquity of wave forms or
cycles. They appear to characterize most living and nonliving
systems. Examples include the Big Bang expansion (and contraction?)

of the Universe, the birth and death of galaxies and stars, glacial
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epochs on Earth, seasons, oscillating chemical reactions, circadian
rhythms, estrus and menstrualcycles, and manic-depressive cycles.
Thus, one should be surprised if-various cycles or waves did not
exist in the socioeconomic macrosystem, not that they do.
Purther,these cycles are usually complex and may differ qualita-
tively on either side to a bifurcation point. For example, the
Pleistocene glaciation was characterized by at least four advances
of the ice separated by at least three interglacial periods. Each
giiacal period was punctuated by at least one interstadial or
warmer period, and each interglacial period by at least one “litle
ice age." A recent report on the origin of the Pleistocene
glaciations [12] shows the influence of exogenous and endogenous
forces, the amplification of the results in changes in Earth's
axis of rotation, precession of the equinoxes, and eccentricity
of orbit, and the reverberation of changes throughout the climatic
system. With minor changes in insolation, the ice-covered area
slowly increased until, castastrophically, the ice tripled in

area and an ice age occurred. Iceberg calving in lakes below the

glaciers led eventually to catasphopic reiz2at of the ice. Both
the mechanisms of system dyncmics and of catastrophe theory are
involved in these realworld phenomena. I believe such a model

also is typical of sociotechnical and economic systems.

Futher, if we consider suddenly falling asleep and sudden
awakening as: behaviors following bifurcation points, the
electroencephalographic wave forms are quite different in the
waking state from the sleep state. In ecosystems different type

waves form (even chaos) may follow critical bifurcation points.

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In many analyses of economic long waves, emphasis is placed
on actions such as maximizing profits. A fuller analysis of human
behavior, for example, the task analysis used in human factors and
industrial engineering, penetrates also into the decisions and
information that antecede actions. We should also note Herbert
Simon's analysis of the classical model of the firm and his replace-
ment of optimizing behavior with satisfying behavior. It may well
be that profit maximization and other simplification are far from

being the major driving forces underlying economic long waves.

In all Communist and socialist countries today, there is
evidence of social malaise and economic, technological, and eco-
logical failures. Consider the bankruptcy of Poland and Romania,
the near revolution in Poland, the chronic shortages of at least
some kinds of food in almost all Communist countries, and the
failures in the production of consumer goods in most of the
countries, It is highly unlikely the economic long waves stem
solely from the inherent déficiencies of Capitalism. There may,
however, be families of long waves, differing from researcher to
researcher as dependent on the particular monetary, industrial, or
technological emphasis. As theory-builders and modelers, we must
be quite certain that we are dealing with the whole sociotechnical
system and not just with selected abstractions as is highly likely
in the absence of a complete historical record. In some cases
model reproduction of historical patterns may be merely coinci-

dental or even tautological.

The range of long-wave periods from 40 to 60 years can
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produce an error of up to 50 percent. This is still a way too
imprecise, and much more must be discovered about the dynamics that
generate such variability. Alternatively, different forces may
operate to produce waves of different duration. If stark non-
equilibrium conditions, bifurcations, catastrophes, and
dissipative structures, as well as equilibrium-seeking, smooth
feedback loops, do play a role in this form of societal evolution,
as I emphasize, then we should attempt to identify the critical
bifurcation points. Examination of a sequence of idealized
Kondratieff waves (see [4] and [11]) suggest for each wave the
sequence: (1) a trough; (2) a less steep followed by a steeper
rise to a peak; (3) a steep decline fromthe peak (primary reces-
sion following a war) followed by a minor recovery; and a steep
followed by a less steep plunge to a trough. Let us assume, for
want of a better starting point, that trough, primary peak, and
secondary peak following the brief recovery are critical bifur-
cation points. Around these points one would expect the greatest
system instability. The critical points could be considered, in
catastrophe theory terms, to be associated with unstable
equilibrium manifolds. The oscillations around the peak especially
suggest conflict between the forces of the old way and those of
the new, which finally prevail. In the simulations of the System
Dynamics National Model, the steep plunges from peak to trough
also suggest more discontinuity than continuity (cf. Figure 2b

an [13]).

In brief summary: the purpose of this rather wide-ranging

discussion has been to caution against both single-cause explanation

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and solely local-cause explanations of societal long waves. I
propose that the basic underlying driving forces in the present
evolution of world society are those fo the life history of human
collective behavior. Human ideas, tools, institutions, and
practices are born, grow, are accepted and developed further, and
diffuse throughout the society, but finally environmental or
inherent structural limits or néw and more competitive ideas, etc.,
appear, which hasten loss of adaptive fit and the decline or
extinction of the old. Much of the theory has, of course, been
proposed by other authors, and the concept of societal stagnation
and aging appears to be firmly embedded in Forrester's theory
behind the Systems Dynamics National Model. ‘Thus, my theory appears
to be broad enough to encompass the areas of concern expressed in
the August and October issues of Futures and in the system dynamics
literature, while at the same time being capable of incorporating
the new constructs of structural stability. We shall examine these
constructs’ and their application to the theory of societal evolution,
particularly to the present stage of world transformation throughout

the rest of the paper.
EQUILIBRIUM, NONEQUILIBRIUM, AND STRUCTURAL STABILITY

It is probably fair to say that equilibrium theory has
dominated most’ of science until very recently. And the concept of
a perturbable equilibrium is closely related to that of systems
stability. Prominent examples include servomechanisms, cybernetic
regulation and control of manned and unmanned vehicles, homeo-

stasis in physiology, and, of course, the "law" of supply and
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demand in economics. Such systems include the large class of
self-regulating systems, which may have very narrow tolerance for
deviation from acriterionlevel. Perturbations that are so
servere as to force the system so far from equilibrium that the
regulatory negative-feedback links are broken usually result in
the destruction of the system (the airplane crashed in turbulent
weather, the patient died from inability to regulate electrolyte
balance, the stock market crashed). Systems of competitive or
conflicting subsystems, such as ecosystems and international
systems, also can show equilibrium behavior and experience the
effects of perturbations that destroy the system and render one
or all populations extinct. This kind of situation is one of
several important to maintaining international stability in the

sense of avoiding war [2], [4], [5].

It is said that equilibrium, a situation in which the system
levels do not change over time and the rates are zero, is central
to system dynamics. Certainly,elementary textbooks such as
Goodman's [14] and broad integrative overviews such as Toward
Global Equilibrium [15] appear to bear out the emphasis. The part
of the logistic curve past the inflection point in the "life cycle
of economic development" (life cycle of a [stage of] a civilization)

is also considered to be moving toward equilibrium.

But recent systems theory indicates the possibility of
several kinds of equilibrium situations. system dynamics deals
with the stable and unstable equilibria and with disequilibria

and unrestrained growth and attempts to restore equilibrium,

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but apparently not explicitly with simultaneous multiple equilibria
and flips among them as in catastrophe: theory or with greatly
displaced nonequilibrium states as in dissipative-structure theory.
These more complex equilibrium configurations can be the basis of
irreversible movements to qualitatively different system behaviors
and even for structural change. Thus, we can contrast the self-
regulation of structually unchanging systems under perturbed
equilibrium conditions as discussed above with the self-organiza~
tion of systems driven far from equilibrium (nonequilibrium

situations) and then perturbed exogenously or made more susceptible

“to endogenous fluctuations.

The need to distinguish among these different equilibrium
situations is not a trivial matter. For example, Mensch, et al.
[16] write of a non-equilibrium theory but appear to be referring
to an economy's proceeding from one disequilibrium state to another.
To me a disequilibrium (out of equilibrium) state potentially can
return to equilibrium, whereas a nonequilibrium (equilibrium
no longer exists or is possible) state can lead to increasing
internal and external fluctuations, to bifurcations, and to struc-
tural change. Further, although Mensch, et al. hint in the
direction of dissipate-structure theory without explicitly
mentioning it or its authors, their concepts of structural stability
and structural change still appear to be undeveloped in the frame~

work of modern structural stability theory.

"Stability" thus also has different meanings. Roughly, it

is the capability of a system to respond to perturbations,
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fluctuations, and random disturbances while still maintaining
about the same dynamic behavior over some period of time.
Stability is often further expressed as local or neighborhood,
global, or neutral stability. Recently, stability has been
contrasted, particularly by ecologists, with resilience, the
ability to absorb relatively strong perturbations without system
breakdown. In the simplest deterministic condition (local)
stability refers to the tendency to return to an equilibrium
point. Lyapunov stability refers to the maintenance close to
equilibrium of the future time-trajectory of a system slightly
perturbed at the origin from equilibrium. Asymptotic stability
refers to the propensity of the system eventually to return to
the equilibrium point. Globally, many system dynamics models

appear to display this kind of stability behavior.

Classical stability may becontrasted with structural

stability [17]. In the former the effects of external perturbations

acting on a fixed system such as a classical pendulum are stressed.

Changes are in the external environment, and the system itself does

not change. Search is for the system's equilibrium points and the
associated dynamic behavior near these points. This approach
would appear to have little relevance to societal systems and

ecosystems functioning far from equilibrium.

The concept of structural stability emphasizes qualitative
changes in the trajectories of the system when the system strucé
ture is perturbed. System behavior is examined with respect to
that of all "nearby" systems. If the behaviors are the same, the
system can be said to be structurally stable. A sufficiently
small perturbation to the dynamics of a structurally stable system

will yield an equivalently small change in dynamic behavior.

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Single or families of differential or difference equations.
can be used to model biological and social systems. The effects
of external perturbations and noise and internal fluctuations on
the stability of the solutions to the equations and presumably on
the structural stability of the realworld analogs can then be
tested. These methods reveal many interesting and unexpected

results, some of which we shall return to later in this paper.

Equilibrium still must be recognized as a powerful attractor
state in systems evolution and behavior. But complex systems
appear frequently to show successive instabilities as the system

proceeds farther and farther from equilibrium. These systems can

be studied by various kinds of bifurcation theory, of which catastrophe
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theory is one specific example. Prigogine [18, p. 105] states

that “in principle, a bifurcation is simply the appearance of a

new solution of the equations for some critical value." ‘Typically,
there are successive bifurcations from the "thermodynamic branch"
or equilibrium state, either branch of which may produce stable or
unstable solutions. The thermodynamic branch describes the solution
to nonlinear equations that correspond to thermodynamic equilibrium
and that can be continued into the nonequilibrium range. Signifi-
cantly, this thermodynamic branch can become unstable at some
gritical distance from equilibrium, presenting numerous successive
primary and secondary bifurcation points. “Such systems involve
both deterministic and stochastic processes. Between the bifur-
cation points, the system appears to obey deterministic laws.

But near the critical points fluctuations exert an increasingly
important influence that determine the branch that’ the system

evolution will follow.

Unfortunately, recent work on chaotic behavior to which we
shall return below, blurs the distinction between determinism
and stochasticity. Nevertheless, it may be that classical system
dynamics is most applicable to smooth periods of growth and decline
[1], [4]. system dynamics may be much less applicable around
critical points and discontinuities and reconfigurations of the
field of forces in societal systems evolution. As some authors

in the August and October issues of Futures question, economic

long waves may not really be wave forms but just such successive

restructurings as I propose.

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CRITICAL POINTS, LINKAGES, AND SYSTEM RECONFIGURATIONS

I believe that search for critical points and neighborhoods
and behaviors characteristic of these domains is now the critical (!)
problem in the study of societal, indeed all, evolution. The
problem can perhaps first be summarized by considering critical
phenomena in physics. Critical.phenomena characterize phase
transitions such as the liquid/gas metallic alloy, immiscible/
miscible liquid, and paramagnetic/ferromagnetic. Superficially
different substances obey the same qualitative and quantitative
laws. We shall restrict our attention to the behavior of (models

of) magnets, especially as sunmarized in [19].

The salient features about magnetism that might be generaliz-
able to societal systems are these, First, behaviorally the
ferromagnet has a clearly identifiable critical point, the Curie
temperature at 1044 degrees K. Well above the Curie temperature
iron displays no spéntaneous magnetization. As the iron is cooled
th the neighborhood of the Curie temperature, there is still no
magnetization. At the Curie temperature magnetization abruptly
occurs, and below the Curie point magnitization increases smoothly.
Second, structurally, well above the Curie temperature little
order exists, that is, the microscopic system constituents, the
magnetic moments of single atoms, are randomly distributed. At
lowest temperatures, longer-range order, correlation among atoms
with the same electron spins, has emerged. At the Curie temperature
these patches of macroscopic order exnand to infinite size and
magnetization suddenly, spontaneously occurs, but fluctuations of
all scales remain. Third, external fields of forces can exert

major effects on structure and behavior.
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Magnetic susceptibility, the change in magnetization induced by a
small applied field has relatively little effect at high tempera-~
tures (the iron cannot retain any magnetization) and low
temperature (the iron is already magnetized and cannot change
much more), But in the neighborhood of the Curie point, either
a small change in temperature or in the external field can give
(catastrophically) a large change in magnetic state. Near the
Curie point, the susceptibility rises “exponentially”: at the

critical temperature itself, the susceptibility becomes infinite.

Fourth, the macroscopic peoperties - for example, correlation
length, spontaneous magnetization, and magnetic susceptibility —of
such thermodynamic systems are functions of the distance of the
system temperature from the critical temperature. Further dis-
cussion of the nature of reduced temperature and critical expon-

ents is beyond the scope of this paper.

Sixth, a coupling strength, K, involving nearest-neighbor
interactions can be defined as the reciprocal of the temperature.
This coupling strength can be changed with a renormalization-

group transformation (successive averaging out of fluctuations)

by which the distance between neighbors increases or decreases.

Only when X continues to equal one, does the critical fixed point
on an imaginary multidimensional surface in parameter space coincide
with an unstable equilibrium. Other values of K may diverge

either toward zero or toward infinity. As in catastrophe theory
and bifurcation theory, and rather counter to system dynamics

theory, systems do appear to be quite sensitive to differences in

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initial conditions.

Clearly, in viewing societal evolution, critical bifurcation
points, can be identified. Beyond these points, some state of
the world is irreversibly changed forever. The easiest points
to identify are military and political, but some economic and
technological points can also be recognized. On December 20,

1860 South Carolina seceded from the Union; on December 17, 1903
the Wright Brothers made their first controlled and sustained
flight at Kitty Hawk, North Carolina, on Black Friday, October 29,
1929, the Wall Street stock market crashed; on September 1, 1939
Aldolf Hitler invaded Poland. Sometimes such events can be pin-

pointed to the exact hour and minute.

It seems to be equally clear that in the neighborhood of
critical points, fluctuations in form and scale increase and that
the susceptibility to system reconfiguration increases greatly.
Unfortunately, most of our knowledge about such behaviors is
derived in retrospect. Rumors of war and increasingly belli-
gerent acts and provocations preceded both the U.S. Civil War
and World War IT, as well as almost all other wars. active trading
by the New York Stock Exchange was several times the normal volume
in the months just before the crash. In our present downturn of
the latest societal long wave, fluctuations in life styles, music,
judicial interpretations, employment, inflation, interest rates,
and business and government practices have been striking. Forrester
[8] writes of the increasing amplitude of business cycles. One

gets the impression today of a changing collective consciousness
24

(an order parameter ‘in the sense of pbysical critical phenomena)
and of a field of forces incipiently preconfigured. Linkages are
weakening among elements and subsystems, but people, at least sub-
consciously aware of imminent changes, are desperately trying to
restore some order and some amount of control over the eroding
old system. The world system-field is now in a critically
metastable state when even slight perturbations or fluctuations

can drive it into a radically different configuration.

A reconfigurating field fo forces’ can be characterized in a
number of ways (see [3], [4], [5] and references therein). Here
we shall be concerned mainly with the formation and weakening of
linkages among elements, changes in system-environment boundary
interrelationships, and forces that push the system farther and

farther into the nonequilibrium region of structural instability.

The system can arbitrarily be considered to span one or
more of the logistic-curve growth stages in the theory of socio-
technical evolution mentioned earlier. Early:in the evolution of
the given system, there may be some partially, viable fragments
of the old system and environment. More importantly, the field is
still susceptible (the climate of collective consciousness is
conducive) to the acceptance and nucleation of social, technologi-
cal, and (formerly in human evolution) biological mutations. Like
some of the authors in the August and October issues of Futures,

I believe that such mutations are clustered in space and time.

Ecological, geographical, and historical reasons for clustering

could be given, but would unduly extend the length of this article.

728

25

Note that this approach is somewhat different from that of Nicolis
and Prigogine [20] whose structural fluctuations, at least in

termite nest-building and army-ant swarming, are randomly distributed.

Nucleations form as a function of both proximity and attrac-
tiveness. The old system-environment boundary interrelationships
have broken down in the domain on either side of the critical point,
and the environment can no longer damp the growing force of the
nucleations. These nucleations may abruptly spread to engulf the
entire system. Eventually, strong bonds are forged among elements
and subsystems of the new system , fostering growth and stability.
Some features of the field of forces may be permanent, for example,
attractors that draw the system toward equilibrium. However,
linkages ultimately age and weaken. It is known from physiology
and psychology that repeated stimulation can lead to saturation of
effect, failure to reinforce, and functional shifts. It is likely
that this is a primary reason for the aging and breakdown of
system linkages, and, in the macrosystemic sense, for the aging
and breakdown of industries and institutions. The system has aged,
become structurally unstable, and is ready for the next reconfigura-

tion.

From'my perspective one of the serious limitations of system
dynamics modeling is the persistence and constant strength of the
linkages in positive and negative feedback loops, which should wax

and wane and perhaps, eventually disappear.

May [21],-in discussing the relationships between system

stability and system complexity, summarizes work on linkages or
26

and ages through one of the stages mentioned earlier, the
stability ~ enhancing semi-autonomous subsystems are lost and

that an increasing homogenization occurs, and that the inter-
connections and the strength of interactions within the larger
system and between the system and its natural environment increase.
With equilibrium configurations limited to restricted ranges of
interaction and environmental parameters (not constants!), with
increasing severity of perturbations and fluctuations, and with

a probable rigidification of present system linkages, it would
appear once again that world society is fast approaching a critical

threshold for reconfiguration.

It appears that stability is a much more complex phenomenon
than was envisioned until recently. In brief: complex systems
can evolve progressively or be driven from regions of narrower

and narrowerer equilibrium-seeking stability to regions of
increasing fluctuations, multiple equilibrium and new organization,
to regions of strangely patterned fluctuation, turbulance, or
chaos and system collapse. Day [22] has reviewed the history of
the concept of chaos and brought it to the attention of system
dynamics audiences. In chaos even simple deterministic nonlinear
difference or differential equations, iterate to depict changes
over time in physical, biological, and behavioral/social systems,
can endogenously generate behaviors that resemble exogenously
imposed random stochastic processes. This finding certainly
provides further ground for debating the “exogeny-endogeny problem"

in system dynamics.

729

27

interconnectively and stability. For example, studies of models
of randomly assembled food webs can be expressed in terms of three
parameters: S, the number of species; C, the average connectance
of the web; and b, the average absolute magnitude of the inter-
action between linked species. Considering the interaction
coefficients ("self-regulatory terms") to be bij = -1, for large S$
the systems will be stable if: b (sc)? <1

Otherwise they will be unstable, that is, increasing complexity
defined by an increasing number of species, or increasing connec-
tance, or increasing interaction strength can decrease dynamic
stability. That is, increasing complexity in these models yields
a dynamic fragility rather than robustness. May defines dynamic
fragility of a system to be stability only witnin a comparatively
small domain of parameter space. in unpredicable environments,
such as the societal environment of today, the stable region of
parameter space would have to be extensive, implying that the

system must be relatively simple.

Empirical tests have been made of the constancy of the
product, SC, as species richness varies [21]. The product has
been shown to be constant, with the underlying mechanism's being
the tendency for larger systems to be organized into small sub-
systems of species, with most interactions taking place within
these subsystems. Thus for given § and C, dynamic stability may
be improved by assembling the food web as a set of loosely coupled
subunits. May's conclusions are strikingly similar to those of
Ashby on loosely connected subsystems and of Simon on the archi-

tecture of complexity. It appears that, as human society evolves
730
28

Of more concern in this paper, however, is the great variety
of forms systems evolution can take, especially as bifurcations
occur more frequently. A review of conditions contributing to

alternate system states has been made by May [23].

Surprisingly complex behaviors can be generated through
iterations of the simplest difference equation:

Keg = PO)
Consider the specific example of the nonlinear function F(X), the
"logistic difference equation":

Neer = Ny (a-b Ny)
This and similar equations contain one or more parameters which
“tune” the steepness of the hump of the curve. For b = 0 anda > 1,
the population grows exponentially. For b # 0, the quadratic
nonlinearity yields agrowth curve the steepness of which is tuned
by the parameter, a. Disregarding some simple mathematical trans-
formations and restrictions on the allowable non-trivial interval
of a, equilibrium values (fixed points) and their stability can
be investigated. For a single-hump curve there is one non-trival
equilibrium solution to X. The stability of the equilibrium
point, X*, depands on the slope of the F(X) curve at X*. At
first, say, at slopes between 45° and -45°, the equilibrium point
is at least locally stable, attracting all trajectories in the
neighborhood. But as the parameter is tuned so that the curve
F(X) becomes even more steeply humped, the equilibrium points

becomes unstable. Successive iterations increase the likeihood of

instability. At exactly this new unstable point, there occur

29

(for Iteration 2) two new and initially stable equilibrium points
of period 2 between which the system alternates in a stable cycle
with period 2. The single-hump curve now has changed to a two-
hump form. Beyond a critical steepness the period 2 points also
become unstable and bifurcate to give an initially stable cycle

of period 4-which in turn yields to a cycle of period 8, and then
to ahirerachy of bifurcating stable cycles with periods 2", that
is 16, 32, 64..... May believes that this process is generic to

most functions F(X) with a steepness of hump that can be tuned.

The range of parameter values that define the stability of
any one cycle progressively diminishes and is bounded above by
some critical parameter value, a point of accumulation of period
2" cycles. This value can usually be calculated exactly. Beyond
this critical point, for example, for a > ac, there is an infinite
number of equilibrium points with different periodicities and an
infinite number of different periodic cycles. Further, there is
an infinite number of initial points, X,, which yield totally
aperiodic trajectories. No matter how many iterations, the pattern
is never repeated. This picture of an infinite number of different
orbits is the "chaos" referred to above. As defined by increasing
values of a, the fixed point becomes unstable before the chaotic
region beings. Also, there are stable cycles even within the
chaotic region. This situation is suggestive of the critical pheno-

mena in physics discussed’ above.

Similarly, the relationship between X,,, (the ordinate) and

(the abscissa) can be obtained by three iterations of the above

730
30

equation. The hills and valleys become more pronounced as the
parameter a increases, and six new period-3 points (points of
intersection with the 45° line) appear. This can be plotted as

two cycles, each of period 3.

May distinguishes between two different kinds of bifurcation
processes for such first-order difference equations. First is
tangent bifurcation, as summarized just abore, in which the hills
and valleys of higher iterations move, respectively, up and down
to meet the 45° line. At the moment these hills and valleys become
tangent to the 45° line, a pair of new cycles of period k, one

stable and one unstable, arises. Pitchfork bifurcation arises when

an originally stable cycle of perion k may become unstable as F(X)
steepens. The slope of the given iteration at the period k points
steepens beyond -1, where a new and initially stable cycle of period

x
2° appears.

There are two critical parameter values: (1) that in the
chaotic region in which the first odd-period cycle appears, and
(2) the point at which the period-3 cycle first appears ("period

three implies chaos").

Most importantly, these seemingly erratic flucuations may stem
from a rigidly deterministic population-growth relationship. For
our purposes, “population” is not limited to numbers of living
organisms, but may apply also to ideas, innovations, strategies,
practices, sociotechnical units, and so forth. Further, in the
chaotic region, arbitrarily close initial conditions may produce

trajectories that eventually diverge widely. Another, perhaps related

31

kind of divergence is seen in catastrophe theory when initially
close behaviors diverge on either side of the manifold. Long-

tert prediction thus becomes impossible.

In studies of fluid turbulence, as a certain parameter is
tuned to a set of deterministic equations, motion can display
an abrupt transition from a stable configuration such as laminar
flow into a chaotic regime [23], [24]. I believe that it is of
paramount importance to search for such critical points in the
turbulent-environmental field of societal science. In evolving
societal systems also an appropriate model might involve the
Sequence: monotonic damping, damped oscillations, stable limit-
cycles, and chaos associated with system collapse and reconfigu-
ration. In higher-order or higher-dimensional systems, chaotic
behaviors may occur under even less severe constraints (e.g., less
severe nonlinearities or less steeply humped F(X)) thanis the case

with the one-dimensional systems summazized above.

As with models, however, the question of fidelity arises
here too. For example, to what extent is the erratic behavior an
artifact of numerical analysis or computer simulation? A number
of realworld physical systems ranging from simple electrical
circuits to complex fluids do show the transition to chaos in
quantitative agreement with the theoretical predictions: There
appears to be a remarkable correspondence with the second-order
phase transitions in magnetism which we discussed earlier under
the topic of critical phenomena, Once again there appear to be

universal numbers for superficially very different systems [24].
71
32

And, very importantly, once again we see a movement toward grand
unifying principles. The onset of trubulence also can be thought
of as a kind of phase transition. It may be described by a suc-

cession df three transitions at most (as above, "period three

implies chaos"). Thus, the transitions to choas themselves may

be orderly and predictable, at least in physical systems.

To conclude, we note that the recent advances discussed in
this section touch on several fundamental assumptions of system
dynamics theory and modeling methodology. These are the insensi-
tivity, with respect to qualitative behavior, of the system/model
to changes in initial conditions and parameter values. Using

more conventional techniques of sensitivity analysis, Vermeulen

and De Jongh [25] also report that qualitatively diffent behaviors
can result from even small perturbations of the system. It may

be that some of the basic theoretical assumptions of system dynamics

should now be reexamined in the light of new knowledge.
EVOLUTIONARY DYNAMICS AND THE MANAGEMENT OF SOCIETY .

A mental synthesis of the many ideas presented in this paper,
and attention to the turbulence in the real world, indicate an
urgency in developing better understanding of the dynamic processes
of societal evolution, our capabilities for building theory about ané
modeling these processes, and the role of our models in the

management of complex systems.

We have taken, as a major mode of reference for societal

evolution during our times, the concept of a series of economic

33

long-waves or Kondratieff cycles. But perhaps, although major
changes in society are undeniable, the concept of continuous
waves in spurious. I believe that a more likely situation is
succesive configurations (structures) of the world societal-field
separated by briefer periods of stark reconfiguration (structural
change) that asymetrically surround critical points of bifurcation,
discontinuity, catastrophe, and emergence of qualitatively new
order. Each configuration eventually ages and wears out becoming
ever more vunerable to exogenous perturbations and endogenous
fluctuations. Of course, any system as complex as modern industrial
society has enough "variables" to present a picture of continuity
even though the major qualitative dynamics are fundamentally dis-

continuous.

Whether the concept of continuous waves is the most realistic
way of describing societal evolution or not, the patterns of
interacting primary industrial (capital sector), secondary industrial
(consumer - goods sector), employment, economic, strategic, human
behavioral, and other factors, verbally described by Forrester in
[7] and [8], provide a powerful basis for further theory- and
modeling building. But there does appear to be a disparity between
these verbal descriptions and the present output of the System
Dynamics National Model. Forrester's theory or conceptual model
appears to be way ahead of the assembled computer simulation model.
Many of Forrester's statement fit in nicely with what I call "field
theory", but I am not certain how well these ideas can be translated
into model struéture. One example is the coupling mechanisms under-

lying entrainment [7, pp. 538-539]. In fact, here is one of the
34

best examples of what is meant by a field of forces. Forrester
writes:".,it is reported that several pendulum clocks in the same
room can begin to swing in unison because of a slight coupling
through the structure of the room." In the entrainment of national

economics, perhaps the concept of an "attractor" --a state that

attracts all neighboring trajectories --would also be of value.
Nevertheless, greater specifications of the entraining force

appears necessary.

Further [7, p. 540], Forrester writes, concerning the upswing
of a long wave: “There is a high degree of unity and interrelated-
ness to all that must happen. ....about half way, the style and
pattern become rigid. ....A radical improvement does not fit...."
The integrating field of forces may well involve collective
intelligence, collective perception, and collective cognitive
exhaustion. And [8, p. 8], Forrester writes: "The long wave is
accentuated by the length of people's memories of past economic
disasters,...." Can these emergent field-theoretic concepts be
explicitly incorporated into the model structure, or must they be

implied as part of the educational and managerial processes?

Further, Forrester [7, p. 541] states: "Research must focus
more sharply on the bridge between micro-structures and macro-
behavior." This, again, ties in with my field theory of

emergent pheromena.

Not only may past long waves actually represent mentally
synthesized segments separted by discontinuties, but the outcome

of the present downswing may be radically different from past

732

35

recoveries. Indeed, there may be no recovery, but rather one of
history's major reconfigurations. This could occur because of the
superposition of several fields of forces. Forrester [7] proposes
a simultaneous occurrence of the long-wave peak and the transition
region (region near the inflection point of a logistic curve) of
the life cycle of economic development (life of a civilization or
major segment of a civilization). He writes: "...our social and
economic system will be buffeted by a combination of forces that
has not previously been experienced" (emphasis added). To these
fields, I add the nonequilibrium structural-stability changes

characterizing the field of forces emphasized in this paper.

Moreover, even if another recovery were to occur, we might
expect it to be qualitatively much different from previous ones.
A major structural change in employment is most likely, a change
characterized by massive social disruption. It is likely that the
major industries of such a recovery would be based on innovations
in robotics, factory automation and biotechnology [26]. These
industries, and their spinoffs and supporting industries, would

hardly be labor-intensive.

The urgency of developing radical new innovations and methods
for societal planning, policymaking, and decisionmaking, in
anticipating and regulating, controlling, and adapting to explosive
sociotechnical and environmental change and reconfiguration, has
been stressed by several authors including me (especially in [3])
and, I believe, Forrester [7] and Holling [27]. Holling reports

on a number of environmental-management policies, all of which were
733
+ 36

"successful" in the short-run but failed in the long run. Each

policy had triggered the system to evolve into one with qualita-

tively different properties.

Finally, can the System Dynamics National Model help fulfill

these urgent managerial needs?

I believe so, but I suggest the

following areas of possible concern and further investigation:

1.

System dynamics, expressing (self) regulation and control,
may be necessary but, by not depicting emergence of new
structure, insufficient for change [1], [3], [4].

System dynamics has traditionally contrasted itself with
econometric modeling, a relatively’ primitive and, I believe,
obsolescent but unfortunately. still politically powerful
methodology. "Classical" system dynamics should now look
at the "other" system dynamics (the dynamics of systems),
some of which has been emphasized in this paper. Perhaps
new insights into improving model structure would emerge.
The system dynamics model, like all such models, is a
sociotechnical innovation. Like weapons systems, power
plants, and so on, a long lead-time is necessary between
conception and fruition. Meanwhile, the real world is
changing rapidly, and these changes lead modeling efforts-

So far 10 years have been devoted to assembling and linking
the capital and consumer sectors. This effort has produced
invaluable new insights. But can the model be completed

in time to deal with today's mounting crises, for example,
permanent massive unemployment, national bankruptcies, and

possible collapse of the national banking system? I have

37

seen many computer programs that have become unknowable
and unyorkable because of superstition of modifications
like the Engineering Change Proposals in hardware design.
4. Perhaps it is no longer possible to complete a complex
computer simulation model of society to be turned over to
"decision-makers." Perhaps the major use of these system

dynamics models is as a heuristic, as has apparently been

the case with the National Model so far, in theory-build-
ing and eventually in interactive problemsolving by

expert advisors in business and government.

5. Perhaps some of the new constructs of system is science can

be applied variously to model simplification, model com-
pletion, and improvement of model fidelity through
internalization of discontinuities, structrual change,

and so forth

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