Table of Contents
ADAPTIVE BALANCE OF CAUSES IN SOCIAL ECOLOGICAL- ECONOMIC
SY STEMS
LETimchenko , E.M.Igumnova and I. Timchenko
Marine Hydrophysical Institute of National A cademy of Sciences of
Ukzaine. 2, Kapitanskaya str. Sevastopol. 99011. Ukraine.
timchenko@ stel.sebastopol.ua
INTRODUCTION.
Any separate part of the populated world temitory represents a social ecological-
economic system, which sustainable development depends on natura, economic,
humanitarian and others resources use. Since the system is being in a dynamic balance
with the complex and changing environment, it is necessay to have predicted
development scenarios as the system possible reactions on changing environmental
conditions. That is the reason why dynamic models of complex socio-ecological-
economic systems became a core instrument of the sustainable development
management Along with these models the informational technologies should be
constructed for the decision making support on rational ways of management.
In this paper we use the Adaptive Balance of Causes (or ABC) method of complex
systems modeling [1], which one could consider as a specific version of the system
dynamic approach [2,3]. To begin with the proposed modeling we need to formulate
several main concepts of system analysis due to their significance for sustainable
development management{1]. These concepts are: relativity of development goals,
integrity of contnllable system, casualty, subordination, dynamic balance and
information unity.
Relativity concept means that development objectives of any system have
uncertainties due to the lack of information about the real and anticipated system's states.
Therefore a part of development resources should be directed to the clarification of
development goals. Integrity concept requires the choice of a minimal set of state
variable vector parameters describing the system’s = goal-seeking += movement
Subordination concept introduces the hierarchy of systems in order of their submission
and makes it possible to link the short-term development scenarios with the long-tem
ones. Dynamic balance concept postulates the stability of general contollable system and
their subordinates, which means that a system must retum to its balance state after
extemal influence on it is ceased. And finally, information unity concept points out the
importance of cunent adaptation of predicted development scenarios to the observed
system’s states.
Keeping in mind these concepts one could develop a dynamic model of any system
in three main steps:
1. Concept model constuction by selection of minimal set of most important
purpose- oriented processes in the system, determination of cause-effect linkages between
them and establishing of extemal driving forces,
2. Concept model formalization, which means writing a sd of differential equations
describing selected processes dynamics and revealing their prognostic scenarios,
3. Determination of model coefficients and developing an agent-based technique for
taking into account specific features of inner processes in the system and its relations
with extemal forcing.
The ABC method was suggested to perform all these steps. In this paper we
demonstrate how it works on an example of a social macroeconomic-ecological system.
1. CONCEPT MODEL CONSTRUCTION.
Consider a macroeconomic system of national economy and define a set of
following processes as the most important scenarios for the system sustainable
development.
1. Capital investments in social sphere,
2. Capital investments in industries,
3. Population living standards,
4, Public consciousness,
5. Parliament pressure on govemment on social issues,
6. Production efficiency,
7. Gross industrial output,
8. Corporations pressure on govemment on industries capital investments,
9. Public social stress,
10. Criminal activity,
11. Education and research,
12. Population purchasing capacity,
13. Average prices,
14. Unemployment,
15. Total demand on goods and services,
16. Total supply,
17. Technological net efficiency of production ,
18. Inflation,
19. Total budget income,
20. Health and ecological safety,
21. Taxes,
22. Central bank interest,
23. Extemal (amy) and intemal (police) security,
24. Budget saldo,
25. State expenditures,
26. Capital investments in environment protection,
27. Ecologists pressure on parliament, govemment and corporations
28. Environmental quality
29. Efficiency of new ecologically approved technologies,
30. Pollutants concentration in environment
31. Public ecological consciousness.
We assume, that this set of processes will be sufficient for sustainable
development management, provided that each of them could be presented with the aid of
some numerical index. The main purpose of modeling will be reaction of these processes
on extemal forcing simulating various changes in govemmental policies on taxes,
inflation, social investments and others.
Due to the large amount of parameters in the system state-variable vector we begin
from the socio-economic part of general concept model, which will contain the first 25
model variables from the general list above. In ABC modeling each of the selected 31
parameters should be checked on the existence of influences on it from others 30
processes. The check-up results for the first 25 parameters are summarized in fig. 1,
presenting cause-effect interactions inside the socio-economic pat of the system.
Numbers in rectangular comespond to the numbers of processes. For instance, the amow,
connecting block 7 with block 19 and marked with sign “+”, means that the process ! 7
“Gross industrial output’ has a positive influence on the process ! 19 “ Total budget
income’.
To simplify the explanation of this diagram we could designate the positive
influence, coming from total budget income as +19. Equally considering, for instance,
influences directed to the block ‘ 3 “population living standards’ we could listed them
as follows: +1 “ Capital investments in social sphere’, - 10 “ Criminal activity’, - 14
“Unemployment’, - 13 “ Average prices’, + 20 “ Health and ecological safety”. Public
consciousness (8), is caused by + 3 “population living standards’, - 9 “ Public social
stress” - 10 “ Criminal activity”, + 20 “ Health and ecological safety”, + 23 “ Extemal
(amy) and intemal (police) security” and others.
Parliament pressure on govemment on social issues (5) depends on: - 4 “ Public
consciousness”, - 8 “
investments’, + 9 “ Public social stress’. Since the public social stress is used to be
accumulated gradually, the parliament reaction on it will have some time to pass.
Therefore, on the way from + 9 to 5 the time delay block D3 has been placed in fig 1.
Another one time delay D; was placed to take into account a finite time, which is need to
tise the education and research levels. Time delay D, put off the gross industrial output
tise as a result of the education and research levels improvements.
The similar explanation could be done to all other linkages shown in fig.1. Note,
that an overall set of positive and negative feed backs, controlling the system, has been
formed in a self-acting way by taking into account all possible influences inside the
system.
The socio-ecological part of the general model contains processes from 26 to 31.
Cause-effect diagram for ths part of the model is shown in fig.2. The underlying idea of
ecological economic systems expresses a general balance condition between economic
profitability of natural resources use and the ecological protection of environment This
could be done by a necessary allocation of state capital investments between industrial
production development and environmental condition recovering and conservation. Since
Corporations pressure on govemment on industries capital
the industrial output makes the main impact on environmental pollution contamination,
some part of its investments should be oriented on natural recovering measures. That is
the reason why the two parts of total capital investments: 2 and 26 are connected by
negative influences.
While the decreasing investments in industries may have a shorttem negative
effect on production output, in a long-term perspective it could lead to the development
of new ecologically friendly and efficient production technologies. We consider also the
public ecological consciousness as a part of the public consciousness with positive
interconnections between them. The higher public ecological consciousness, the stronger
public and ecologists pressure on parliament, govemment and corporations resulting in
the increasing of capital investments on environmental protection aims .
Two factors make the concem of ecologists and the society as a whole:
environmental quality 28 and environmental pollution concentrations 30. Environmental
quality improvement could be achieved only with some time delay D,. Two othes
delays, which were introduced on the diagram in fig. 2, are connected with the
decreasing of pollution concentrations by the development of ecologically friendly
industrial technologies (D5) and their implementation (Ds).
2. CONCEPT MODEL FORMALIZATION.
To produce a dynamic model of the social ecologicaleconomic system one should
exploit some method for balancing rates of changes of all the processes with these
processes itself. It should be taken into account also the influences on these processes
coming from inner and extemal sources. The system dynamics (or SD) method has been
successfully applied to solve this problem in numemus works [2,3]. The SD approach
gave rise to the development of a variety of standard sub models (“molecules”) which are
separate blocks of complex stocks and flows diagrams [4]. The overall idea of SD
approach is to find out and use in a model construction a general balance of positive and
negative feed backs, which results in chains of different equations, derived for temps and
auxiliary information transforms.
In a contrast with SD approach in Adaptive Balance of Causes (ABC) method we
have suggested a standard module equation, which could be cunently used for all of the
modeling processes. We assumed, that any process in the system is being in a state of
local dynamic balance with influences applied to it from neighboring processes and
extemal forcing.
Consider a system with n-component state-variables vector, presenting the
processes X;, X2, ...., X,, Which are to be controlled. The standard equation for the
process x, has the following form in ABC method [1]
dx, /dt =[1 - 2F% Oy +ap% +a3% +... + aink TY] ())
where F® is co-called “basic influence function’ - a positive rising function of the
process xX; itself and all influences applied to it Influence coefficients a,,
(pq = 1, 2, ..., n) present the rates ai,X, of intemal cause effects on x;. The item y;
means extemal forcing on x1.
As it was shown in our reference works [1,5] the standard equation (1) has two
important features:
1. It keeps a stable balance state in the absence of extemal influences,
2. It enables to follow for the extemal influences by an adaptation to them.
One could choose in (1) a various types of basic influence functions. For instance, the
most simple one choice is
FO(x, + ax tarks +... + ainXa +yYi) =X + aX + aigk +... +ain%s +1.
It leads to the nonlinear Bemoully equation [1], which is used to be exploit in some
economic and ecological case studies (see, for instance, the Lotka-Voltera equations in
“predator-prey” models [5]). In our case the standard equation takes the form
dx, /dt =x [1 - 20% + ax + aX +... +anx, ty] (2)
With the use of equation (2) the problem of dynamic model construction could be solved
in rather easy and straightforward way.
Let us apply the standard module equation sequentially to all of the processes x,
(i = 1, 2, .. , 31) introduced above for the social ecological-economic system. In
accordance with the system concept model shown in fig. 1 and fig.2 we shall have the set
of 31 equations of the similar fom
x, /dt =x [1 - 20% + ay 2X - ay 5X5- @oXi9- YI,
Ax, /dt =X 1 - 20% - a2 6X - Apig%ig~ @ 2% - Yad],
x ft =x [1 - 20% - a 1% +.Asr0X10 + 5 13%13 + Ay aX - A 20%20- Vad,
xs /Ot =X, [1 - 2(x - ayo - Aa 1iX11 +4 10K 10 - At20X 20 - 43K 3j - A123 a3- Yad],
dxs /dt =x, [1 - 2
xg /dt = x5 [1 - 2
(% + a aX +3 0% - ag D3Xo)],
(
x; /dt =x, [1 - 2(% - @ 6X6 - a7 1sKis- Yr),
(
(
Ne - 2% - Ag 3X - AguiXi1- 17 X 17 - A 20X20),
x, /dt = xy[1 - 20% + a 7X - Ya),
AX, (dt = % [1 - 2(% + 1% +A 4X - @uX4- Vo)l,
X49 /Mt = Xo [1 - 2G + 03X34 aio 23%3 - AiouXu- Yio),
xq, /Ot =X [1 - 266) ~ Ann 12Dz Xp @11Di%- Yd,
AXy2 (dt = Xi2[1 - 2G%2 - Ara sKy t+ a2 10Xig + 12 13X13 Vid],
x13 /dt = x1s[1 - 2(Kis + aig 16X16 - G13 1X19 - 13 21X01 - Big 20%2- Gig iskis - Vis),
x14 [Ot = Xia [1 - 2(Kia + aig 2K + Qa 11%1 + G147X7- Yia)],
xis /dt = xis [1 - 2(Kis - aig a - G15 12%2 + a5 13X13 - Vis),
Axyg (dt = Xe [1 - 2%e - Are Xr - G6 1X17 - Yio),
x7 /dt =%7[1 - 2047 - 7 Xi - Yo),
Akg /dt = Xp [1 - 2(%g + AgiX7 + Aig Xa - Vis),
Axi9 [dt = xig[1 - 2(%9 - Aig iX7- @io2%Xi - Yio), (3)
Axy9 [At = Xoo [1 - 20% - Ao 1X1 - Ao 11X11 > 0 12X12- Yoo],
Axa, /dt = Xi [1 - 2(Ko1 + 1 24X24- You),
(
(
(
(
(
(
(
(
(
2¢
nN
NN
N
Axx2 /dt = Xp [1 - 2(Ko2 - Are 16X18 - Yo2)],
x3 /dt = %3[1 - 2(%3 - a3 2X1- Yos)],
x44 /dt =X),[1 -
dx)5 /dt =x 5[1 -
Axy¢ /dt =X, [1 - 2
AXy7 ft = %7[1 - 2
Axog /dt =xXg[1 - 2
Axg9 /dt =xXo[1 - 2
x30 /dt = xX30[1 - 2
x3; /dt = xy) [1 - 2(%1 - 51 aX4- 831 30830 + O31 26X08 - Vaud],
D, =[1- exp(- djt)], ( =1,2,3, 4,5,6).
The dynamic model (3) has the obvious uniform structure. It could be used for prognostic
scenarios calculation in the considered social ecological-economic system.
3, DETERMINATION OF THE MODEL COEFFICIENTS.
N
Xoq > Ang Ki + Ay 25%05~ You],
Xs ~ @5 1X1 ~ @52X>- Yos)],
Kop + a5 2X ~ 6 27%7- Yoo),
Xo7 > p7 36X30 > A27 3iXs1 - Yor),
N
Mog - Gg 26D4 X26 - 86.29X29 + Ay6 30X30 - Yo8)],
Yoo - a9 26Ds Xy6- Y29)],
Xo - 30 7X7 + B30 29X29 + Ayo 28X28 - Yoo),
The model (3) has an advantage of the ABC modeling method, because it allows
for an objective determination of all coefficients a,, by reanalysis of past (archival)
scenarios of the processes observed. Moreover, the cument evaluation of coefficients is
possible and hence these coefficients could be made variable. That means that linear
approximation of cause-effect interactions inside a system, which was assumed above,
becomes in fact more realistic non-linear.
To achieve the cument coefficients evaluation on observed scenarios one should
make an assumption that cause-effect linkages inside a system are changing more slowly
than the scenarios itself. Then the comelations between archival scenarios x, and extemal
forcing y, must be introduced as follows: Kp, = E{x,x,} and Nyq = Ef{x,yg}. By applying
the Kolmogorov’s optimal interpolation scheme [6,7] one could obtain a set of linear
equations for determination of coefficients in each of equations (3). These sets of
equations take the following general form [1]
Ya Kam =Kin +N, (,m,n=1,2,...,31), (a m,n lin >). (4)
Examples of this technique implementation could be find in our reference works [1,5].
Another one opportmity to make the model (3) more realistic consists in an
intoducing of intelligent agents contolling cause-effect interactions inside the system.
Fist of all agents may be watching for extemal conditions when the system cames on the
edge of destroy of its structme. For instance, the unemployment grow may be followed
by the fall of public consciousness x, much low the some threshold leva x," resulting in
general economic disorder, ceasing the total demand on goods and services Xi5, and
stopping the gross industrial output x; This situation could be accounted for by the
simple agent elements controlling influences of the total output a, jx, on unemployment
X,y total supply x;¢ and inflation x,,
ay7 = IF[Xy >x: then a,;; otherwise a,,exp(-a, t)], (p =14, 16, 18).
More complicated multi-agents control structures were suggested in our reference
works describing the information technology ABC AGENT [5,8]. This technology
implies standard operations taking place in any economic system, which input
depends on the situation at resources markets and output is forced by the situation
at goods and services markets.
The implementation of variable influence coefficients and addition of agent-
based coefficients control results in the much more complicated ABC model for
the system under consideration. But the complication of model based on the
original set of equations (3) is justified by the more adequate model representation
of the social ecological-economic system, which is very much complex in reality.
4. SIMULATION EXPERIMENTS WITH THE MODEL
Simulation experiments with the finite-difference version of the model (3) showed
that it has properties of robustness to the variations of coefficients and rapid convergence
to the balance state from an arbitrary initial condition The model was used to study
reactions of the social ecological- economic system on different management operations.
Socio-economic parts of such systems are used to be very sensible to the capital
investments in social sphere x, inflation x, , total budget income Xo, taxes %, and
central bank interest x... Calculations were made on 150 steps in time and _ influence
coefficients were chosen to meet the required sensibility. Time delays D, (p = 1, 2, ..., 6
system) were ranged between 10 and 40 time steps. We cite below only two of simulation
mms result, which could be called “pessimistic” and “optimistic” development scenarios.
More information could be find in our work [1].
To study pessimistic development scenarios the extemal forcing yj, = Xie’ was
applied to the inflation index x,,. That was done to simulate an unjustified high level of
the money emission with the maximum on 75 time step. The resulting inflation scenario
is shown in fig. 3 along with the unemployment level x4 and central bank interest x.
Noteworthy, that maxima of inflation and unemployment have backwards in attitude on
the money emission maximum. Fig. 4 demonstrates a big rise of public social stress Xo,
caused by the unemployment, and associated grow of ciminal activity Xio, decreasing of
education and research x,; and worsening of health and ecological safety index X9.
For an “optimistic” way of socio-economic development the lowering of taxes
index x, has been chosen. The extemal management function y,, = X»1" presented in
fig. 5. One can see that the minimum of the resulting central bank interest values scenario
has a time lag in comparison with the management foring. That is an evidence of the
system’s resistance to the changes of its dynamic balance state. In accordance with the
decreasing of the central bank interest the economic paramelers grow was achieved and
inflation and unemployment were downed. Scenarios of population living standards x;
and public consciousness x, demonstrate the great improvement That is the reason why
the parliament pressure on govemment on social issues x; was weakened during this time
period.
CONCLUSION.
In this paper we tied to expose the innovated approach to the system dynamic
method which we have called Adaptive balance of causes (ABC). This method is based
on the assumption that any complex system consists of many local balances, which could
be presented by a standard module equation in the system model. The main property of
the module is the prompt adaptation of its balance state to the changing influences
coming from neighboring modules and extemal forcing applied to the system. In our
view point a complex socio ecological-economic system consists of the standard modules
expressing an adaptive balance of causes.
An obvious advantage of such representation is the simple and direct construction
of a set of dynamic equations for socio ecological-economic processes based on a cause-
effect diagram of the system. We believe, that this property of ABC modeling was wel
illustrated by the transition from concept model presented in fig. 1 and 2 to the set of
equations (3).
Another one advantage consists in objective evaluation of the model coefficients
by the reanalysis of archival scenarios of the system behavior That allows for to
introduce in a model not only objective, but variable coefficients and hence to ensure
more realistic non-linear modeling. We convinced, that this opportunity of the ABC
modeling could be very useful in the processing of archival information about the socio
ecological-economic dynamics in geo information systems (GIS).
The ABC modeling approach supposes also the use of intelligent agents for
executing necessary control operations with the model influence coefficients. While
standard modules ensure the adaptation of development scenarios to the cunently
changing situation inside and outside of the social ecological-economic system,
intelligent agents are watching the changes and making prescribed them actions. That is a
farther way to more realistic and reliable scenarios prediction in such systems.
We have discussed the implementation of the ABC method to the mode
construction of a social ecological-economic system. This case study served only to
illustrate in brief three main steps of ABC modeling outlined in the intoduction to the
paper. More information about this study one could find in our reference works.
REFERENCES
1. Timchenko LE, EMIgummova and I1'Timchenkn System management and ABC
technologies of sustainable = development. “Ecosy- Hydrophysics” Publisher.
Sevastopol, 2000, - 225 p. (in Russian).
2. Forrester, J.W. Principles of Systems. Cambridge MA, Productivity Press. 1968.
3. Sterman, J.D. Business Dynamics: Systems Thinking and Modeling for a Complex
Word, —Irwin/McGraw-Hill. 1999.
4, Gilbert N. and K.G Troitzsch. Simulation for the Social Scientist. Open University
Press, 1999.
5. Timchenko LE, EMIgummova and SMSolodova Natural resources management.
Simulation technology ABC AGENT. MHI Publisher. Sevastopol, 2001, 96 p. (in
Russian).
6. Tumchenko LE. Stochastic Modelling of Ocean Dynamics // Harwood Acad. Publ.
Chur- London-Paris-New- Y ork, 1984. - 320 p.
7. Timchenko LE and EMlJgunmova Natural resources management in ecological
economic system. // Marine Hydrophysical Joumal, 1999, 1 6 p. 30 - 45. (nm
Russian).
8. ‘Timchenko LE, EMIgummova and [1Timchenkn Dynamics of ecological- economic
systems. In: Ecological safety of sea shore and shelf zones and effective use of shelf
resources. MHI Publisher. Sevastopol, 2001, p. 62-77 (in Russian).
Fig. 1. Concept model of the system’s socio-economic part.
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INVESTMENTS DELAY IN NEW
INENVIRONMENT }—&— | TECHNOLOGIES
PROTECTION DESIGN
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Fig. 2. Concept model of ecological-economic subsystem.
Numbers of model parameters are in circles.
—O—X 14
EX as
AX 22
v
—%-X 1s
Fig. 3. Simulated money emission variation (X 1¢) and associated
inflation (X19).
2 50 7 100 125 150
Fig. 4. Social stress scenario (X 9) under money emission variation.
T 1
25 50 Dd 100 125 150
Fig. 5. Simulated variation of average taxes rate (X41).
ie} T T T T T 1
2 50 7 100 125 150
Fig. 6. Living standard (X 3) and social awareness (X 4) under
taxes rate variation.
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