Landscape Delimitation between Ethnoses by Modelling
Victor V. Korobitsin and Julia V. Frolova
Omsk State University, Computer Science Department,
55A, Mira pr., 644077 Omsk, Russia
phone +7-3812-647200, fax +7-3812-223883
korobits@univer.omsk.su
frolova@univer.omsk.su
Abstract. The aim of presented research is the construction of mathematical model of ethnic
field. The model is described by the system of parabolic equations. It is the tools for research the
evolution of interactive ethnic systems under landscape influence. The ethnic system includes
a few ethnoses and provides their interactions. The interactions transmit by ethnic fields. This
model describes the behavior of society on ethnic solidarity level. The software TERRI is used for
the forecast of arising the ethnic conflicts. We carry out analysis of simulation results of ethnic
fields: ethnic map coloring; delimitation three borders between super-cthnoses on the ethnic map
of investigation region; comparison the experimental data with the facts; relationship of ethnic
fields model with real ethnic processes. Based on simulation result the researcher can compute the
direction of ethnic field distribution and the most probable points of skirmish between ethnoses.
1 Introduction
The modelling of biosphere (ecological) processes gave rise to the research of society development.
These models were destined for solving the problem of global change the ecological situation. Now the
problem of interethnic conflicts is growing in society. It forces the international organizations to find
the way for its adjustment. The modelling of global ethnic processes will allows to evaluate the world
ethnic situation.
The aim of this research is the construction of mathematical model of ethnic field. The model is
described by the system of parabolic equations. It is the tools for research the evolution of interactive
ethnic systems under landscape influence.
2 Ethnic Solidarity Level
On the ethnosphere level the traditions play the special role in the society. The people get the behavior
stereotypes from them. Thereby the general function of this level is the sample maintenance. The
individuals strive for conservation of culture as a collection of history experience.
The ethnos is a people group, formed on basis of the original behavior stereotype. It exists as a
energy system, opposing itself to other like groups. Thereby people are divided on own and alien man.
The main ethnos attribute is a behavior stereotype. It is a complex of behavior standards of ethnos
members. The collection of behavior stereotypes is defined by ethnic tradition differed the ethnos from
biological population.
The passio energy is an excess of biochemical energy of living substance. It suppresses the self-
preservation instinct of man and defines the ability to goal-directed ultratension. The ethnic field is
formed by the passio energy. It provides the interaction of ethnos members and regulates the joint
goal-directed activity of their. Each ethnos forms the unique field and each ethnos member responds
to this field. The behavior stereotypes, landscape, and culture values of ethnos characterize the field
influence,
The primary motive for arising the ethnic conflicts is a skirmish of two not solidary ethnoses. The
skirmish is an effect of distribution of some ethnic field on the territory of another ethnos. There are
the territories occupied by the people of different ethnic systems. Such territory is a border or buffer
2 Victor Korobitsin and Julia Frolova
zone placed between two ethnoses. The ethnic conflicts mostly arise on these zones. Therefore the
actual problem is to discover the buffer zones and to forecast the ethnic conflicts. For this problem
decision, we propose to use the methods of mathematical modelling. The model of level is created on
the basis of Lev N. Gumilev’s theory of ethnogenesis [1].
3 Mathematical Model of Ethnic Field
The ethnic system includes a few ethnoses and provides their interactions. The interactions is trans-
mited by ethnic fields. This field is distributed on the landscape as hot gas in the space. We constructed
the model of ethnic field from this analogy.
Consider the interaction of k ethnoses in the field G C R? with boundary I. Let the pass
of i ethnos (U;) satisfies the energy conservation law in any given area. Define the passio energy density
uisby
Uilt) = I/ saga aged ace,
G
The ethnos state is defined by the passio tension. This characteristic is the ratio of passio en-
ergy volume to ethnos population quantity. The function E(x, y,t) passio tension of ethnic field is
energy
constructed on base of the measurement strategy of history events frequency.
Interrelate the passio tension and density u(x, y,1) of ethnic field energy by
u(x, y,t) = ksq(x,y,t)B(x,y,t),
where q(x, y, t) is the density of field receptivity by ethnos members, ks is the coefficient. The function
a(x, y.t) is defined by the relation
Q(t) = 225) = | f a(x, y, t)dedy,
Tas ff
where the function Q;(t) describes the degree of receptivity and goal-directed use of passio energy by
j'® ethnos member. The summation is made on all ethnos members fallen in G area.
Construct the integral balance equation describing change to density of ethnic field energy uj (x,y, t)
of i‘ ethnos (i= 1,...,k), k is amount of ethnoses.
ty
Uj (t2) — Viti) = [|r + Pi(t) +7; (t) +7; (t) + Ki(t)| dt, (1)
4
where U;(t) = ff ui(z,y, t}dzdy. The flows of passio energy are described by following expressions:
G
— R; is the passio energy inflowing in G through boundary I’,
Ri(t)= f alent) Pteuttr
r
the coefficient ¢;(z, y,t) characterizes the velocity of passio energy distribution.
— P,(t) is the passio energy inflowing in G under the influence of directional moving energy through
boundary I’,
Fd) = f ~laimuey tar,
F
the vector field a; gives the direction of energy moving, the vector n is exterior normal to boundary
section dy. Let rot a; = 0 then the scalar function ¢; exists and a; = —grad yi(2,y, t).
Landscape Delimitation between Ethnoses by Modelling 3
— T;*(#) is inflow of passio energy under the induction process in G,
TH) = ff it (2-a.t\oa(e. ytd
G
the coefficient 47 (x.y,t) is the velocity of induction process.
— T(t) is outflow of passio energy to life support of ethnos members and landscape maintenance,
Tr (t)= ff -% (x,y, t)ui (a, y, t)dedy,
G
the coefficient > («, y, t) is the velocity of passio energy losses.
— K;(t) is outflow of passio energy under the skirmish of two ethoses,
Ki = If - (= ij (a. y,t)u;(a, y.t))ui (x.y, t)dedy,
G a=
where w, is the density of passio energy of hostile ethnos, the coefficient +, (a, y.t) is the velocity of
energy losses under the rivalry i” and j*”" ethnoses. The ratio ;;u? describes the internal conflicts
in ethnos.
The system of integral equations (1) is equivalent to the system of parabolic differential equations
(add see Guts et al. 2000. [3])
du _ 8 (B91, Ou) 8 (Oe BW) (ps 9-5,
T= Be gam tess) + (eu test) + (03 B; dw ui, (2)
Define the initial and edge conditions for the system of parabolic equations by
uj(a,y.0) = uf (x,y), (vy) € G,
Se (x,y.t) =0, (wy) el. (3)
Define the functions as follows:
— moving the passio energy
Xr 5 )
gila.y) = He I, Mi > 0. pi > 0, (29, ¥?) EG,
i
— the passio energy distribution
ei(a.y) =Iq(,; olu)(z.y), laiwoL, &,:L—> Rt,
where w is the discrete grid on G area, Iq is the interpolation operator of discrete functions on w
to continuous functions on G, L is a set of landscape types,
— outflow of the passio energy
Be (w,y) = Ta (sr ole)(m.y), Ga: L > RY,
— inflow of the passio energy
BF (t) =max{0, 6) -— 8 -(¢-T)}, BBE Rt, Th >0,
— the passio energy losses 7ij € Rt.
The system of parabolic differential equations (2) with the initial and edge conditions (3) is a
mathematical model of ethnic field interactions.
Given model is a way for formalization of Lev N. Gumilev’s theory. The model accentuates the
energy and geographical aspects of theory and gives the clear formal description of internal processes.
4 Victor Korobitsin and Julia Frolova
4 Simulation Tools TERRI for Modeling the Ethnic Fields
The simulation tools TERRI is created for modeling of ethnosphere level. The tools realize the method
for solving the system of parabolic differential equations that described the model of ethnosphere. The
modeling result is demonstrated on the computer display as a dynamic map of ethnic fields.
The initial data for modeling are the number of ethnoses k, map of landscapes, rates of changing
the passio energy (functions ¢;, yi, 8i, 7ij), initial distribution of passio energy density u?.
Consider the simulation result of ethnosphere on real example. The aim of simulation was to define
the landscape dependence of division of territory between ethnoses. The dependence is discovered on
real geographical features of Europe, North Africa, and Middle East. Examine the interaction of three
ethnic systems: West European, East Slavonic, Asia Minor. Each ethnos was described by the set of
features (the function in the system (2)).
After run the modeling software TERRI, the map of landscapes is appeared on the display. On this
map the different landscapes are marked by various colors. The ethnos is born in some point on the
map. So the ethnic field is got the initial pulse. According to dynamic rule (2) the field is distributing
on the landscape. The ethnic field is marked by color area on the display. Each ethnos has own color:
first. ethnos — blue, second — red, third — green. Given picture is demonstrated the distribution of
ethnoses on the landscape. The value of passio energy density is shown by the brightness of color. The
three stages of ethnos dynamics is shown on figure 1.
© West European ethnos @ East Slavonic ethnos @ Asia Minor ethnos
Fig. 1. Distribution of ethnic fields
Initially the born ethnoses is developed on the isolation with each other. In time they come into
collision observed by the ethnic field crossing. Under conflicts the passio energy of hostile ethnoses is
loss. Since there are not solidary ethnoses then all they can not coexist on common territory. We can
observe two way of conflict adjustment. Either the most powered ethnos forces out the feeble one or
the equal-powered ethnoses separate the landscape. The buffer zone is formed between them.
The software TERRI allows doing a lot of tests with model. We fixed the part of initial parameters
but were changed other parameters in various tests. We were getting the various pictures of ethnic
dynamics. For analyzing the model behavior we was collecting the data of ethnos field distribution.
The statistical analysis is demonstrated the dependence of ethnic field distribution on the landscapes.
5 Analysis of Simulation Results of Ethnic Fields
5.1 Ethnic Map Coloring
The simulation result is the statistical distribution of super-ethnoses on the landscape (figure 2).
The experimental data are given in table 1. Here, the values are the probability of events Aj;
(%). Each event Aj; signifies that i-city will pertain to j-ethnos, here i = 1,2,...,80, j = 1,2,3,4.
Moreover the mark 4-ethnos points to case where the city is free from presences some ethnos from
three determined ethnoses.
Landscape Delimitation between Ethnoses by Modelling 5
Table 1. The Simulation Results of the Ethnic Fields. Super-Ethnos: I - West-European, II - East-Slavonic,
III - Asia Minor, IV - other.
Seville Madrid
Vigo Bilbao
Valencia Andorra
Toulouse Marseilles
Limoges Geneva
Paris London
Glasgow Cologne
Stuttgart Munich
Milan Venice
Florence Rome
Taranto Palermo
Sassari Copenhagen
Hamburg Berlin
Prague
Zagreb Sarajevo
Oslo Stockholm
Malmen Kaliningrad
Warsaw Krakow
Lvov Budapest
Belgrade Skopje
Saloniki Athens
Sofia Bucharest
Istanbul Imir
Novgorod Minsk
Kiev Kishinev
Crimea Kharkov
Moscow Volgograd
Rostov Astrakhan
Krasnodar Cherkessk
Terrible Makhachkala
Batumi Tilisi
Yerevan Baku
Ardebil Teheran
Mosul Haleb
Adana Samson
Bursa Damascus
Baghdad Jerusalem
Cairo Tunis
Algiers Oran
Rabat Safi
6 Victor Korobitsin and Julia Frolova
1 2 3 4
Fig. 2. Statistics of Ethnos Distribution
We give the comment of data. There are the cities, where single ethnos predominates over all
other with more probability. For example, cities: Paris (West-European - 87.2%). Stuttgart (West-
European - 88.2%), Rome (West-European - 78.4%), Kiev (East-Slavonic - 80.8%), Moscow (East-
Slavonic - 76.8%), Minsk (East-Slavonic - 82.2%), Kishinev (East-Slavonic - 77.2%), Terrible (Asia
Minor - 60.8%), Haleb (Asia Minor - 93.6%), Izmir (Asia Minor - 73.2%), Adana (Asia Minor - 92.8%),
Damascus (Asia Minor - 92.6%).
The cities are free if the probability of this event most (none of ethnos does predominate). These
cities are located far from birth-places of ethnoses. So for the simulation period at 500 years, none
of ethnos does have time to its occupy. For example, cities: Seville (free — 73.6%), Glasgow (87.2%),
Oslo (91.2%), Stockholm (87.4%), Algiers (79.8%), Rabat (88.6%), Teheran (78.0%), Tunis (78.8%),
Oran (83.6%), Safi (100%). These cities are located on lands of our map.
There are the cities pertaining to two ethnoses with equal probability. For example, cities: Belgrade
(West-European - 46.4%, East-Slavonic - 46.6%), Volgograd (East-Slavonic - 46.0%, Asia Minor -
46.0%). But there are cities, where three ethnoses share between themselves city. For example, cities: :
Skopje (West-European — 36.0%, East-Slavonic— 34.0%, Asia Minor — 30.0%), Saloniki (31.8%, 35.4%,
32.8%), Sarajevo (49.2%, 32.2%, 18.6%), Athens (33.2%, 33.0%, 31.6%). These cities can pertain to
any ethnoses nearly with equally probability. In real situations this means that the representatives of
all ethnoses live on territory of this city in equal portion.
The analysis of computer simulation results allows doing the following conclusions:
— the distribution of territories between ethnoses really depends on landscape;
— the obtained statistical data demonstrates the correlation of settling the ethnos on landscapes;
— the size of buffer zone is depended on the hostility of neighbor ethnoses.
Landscape Delimitation between Ethnoses by Modelling 7
5.2. Comparison the Experimental Data with the Facts
The comparative analysis of experimental data with the facts was made for the confirmation of hypoth-
esis on ethnos distribution. The experimental data were collected by the software TERRI. The facts
are the percentage composition of population by church in the cities of region. These data was given
from electronic library of Utrecht University, The Netherlands. The result of comparative analysis is
shown on table 2.
The cities on table is sorted in ascending order of value A. It is a deviation of experimental data
from the facts, defined by
4
=p lh
where a; is the facts, bj is the experimental data, i is super-ethnos number.
Table 2. Experimental Data vs the Facts. Church: I- Roman Catholic, II - Orthodox, II - Islam, IV - other;
Super-Ethnos: 1 - West-European, 2 - East-Slavonic, 3 - Asia Minor, 4 - other.
City T mii] i 2 3 4, 4
Paris 89 4 3 4/872 80 00 48] 48
Andorra 86 0 O 14/768 58 0.0 17.4] 9.2
Zagreb 77 11 0 12/688 29.8
Rome 83 0 O 17/784 14.0
Buchares 6 80 O 14]22.8 71.6
Minsk 8 60 0 32]15.6 82.2
Vienna 8% 0 0 15/648 35.2
Sarajevo 15 31 40 14/49.2 32.2
Sophia 1 87 8 4/350 49.8
Prague 502 0 48/662 33.8
Berlin B70 2 61/606 334
Athens 0 97 1 2433.2 33.0
Budapest |68 0 0 32]35.6 64.0
Tbilisi 0 75 11 14] 0.0 10.4
Copenhagen] 1 0 0 99]60.0 11.8
Jerusalem 0 3 15 82] 04 00
Yerevan 0 100 0 Of 00 68 71.0 22.2 | 93.2
At the top of the table the are cities, where experimental data nearly equal with facts. The cities
with wide discrepancy are at the bottom of the table.
In table by line we separate the cities with value A > 50% Why we have got strong divergence?
The main reasons are two:
1) under consideration area is confined and we investigate only super-ethnoses behavior.
2) there is a difference between the membership of ethnos and the composition of population by
church in the cities of region.
We will demonstrate these reasons on examples. Berlin is the first city below line. Obviously
the population of Germany pertains to west-european super-ethnos (experimental value 66.6%), but
Roman Catholic church is not topping at this state (facts 37.0%). This implyies large deviation of
value A. Same reason influences on result of experiment at city Copenhagen.
Next city is Athens. Main composition of population by church is Orthodox (97.0%). But geo-
graphical location of Greece points that all ethnic of group can live on its territory. It is demonstrated
in calculations (West-European - 33.2%, East-Slavonic - 33.0%, Asia Minor - 31.6%). Similar dispar-
ity observes between territorial location and composition of population by church at cities Yerevan,
Tbilisi, Jerusalem, Budapest.
8 Victor Korobitsin and Julia Frolova
5.3 Analysis of the Points of Skirmish between Ethnoses
According to results of computer experiments (fig.2, table 2) we have got three borders between
super-ethnoses on the ethnic map of investigation region:
1. West-European - East-Slavonic;
2. East-Slavonic - Asia Minor;
3. West-European - East-Slavonic - Asia Minor.
The First border passes on cities of East Europe from Baltic Sea to Adriatic Sea: Kaliningrad, Warsaw,
Crakow, Budapest, Belgrade. It point to the separation of Europe on west and east. (west-european
and east-slavonic super-ethnoses). The Second border passes on south part of Russia from Black Sea to
Caspian Sea: Crimea, Krasnodar, Rostov-on-Don, Volgograd, Astrakhan. Here the east-slavonic super-
ethnos is contiguous to the asia minor super-ethnos. The Third border passes on Balkan Peninsula
from Mediterranean Sea to Black Sea: Sarajevo, Skopje, Saloniki, Sofia, Athens, Istanbul. This is the
domain of covering three ethnic fields. Here all three super-ethnoses wield influence.
So, this investigation shows the influence of geographical particularities of landscape on behavior
of ethnic fields. We found the separation of map on ethnic regions with defined borders. These borders
define the points of skirmish between super-ethnoses. The ethnic conflicts have the most probable
nearly these borders. The military conflicts are as a result of the surge of ethnic energy on border of
two ethnoses. But if both ethnoses are enough mighty, then long hostilities occur.
Existence of these borders in reality is confirmed the multitude of examples from world history.
So, the opposition of West and East Europe exists over the long years. Other history examples: the
military conflicts on Transcaucasia, the war on Balkan. Moreover the last example is most vehement
strife. As here three super-ethnoses come into collision.
5.4 Relationship of Ethnic Fields Model with Real Ethnic Processes
The presented model can be an exact prototype real development all super-ethnoses. The reason of
disparity is a simplification peculiar to any model. We will point on some neglible reasons at this
model. Apparently, they influence on development process of ethnoses:
1) the ethnic system is subsystem of society. Society system consists of the following levels: biosphere,
ethnosphere, sociosphere, psychosphere, anthroposphere.
2) ethnos as complex system has own structure with following subsystem: passionary, harmonious
people, sub-passionary, organization, science and technology, culture and art, landscape.
In spite of the reasons, we have got enough adequate model of complex process of development of
ethnic fields. The results of modeling and comparison them with fact data allow us to say that model
reflects real ethno-social process.
6 Conclusion
We constructed the mathematical model of ethnic system. On results of presented research we can
make up the following conclusions:
— this model is the tools for investigation in global development. society area. Based on simulation
result the researcher will have got the numerical evaluation of historical hypothesis on ethnosphere
evolution;
— the software TERRI is used for the forecast of arising the ethnic conflicts. In that case, it is
necessary to keep track of the passio energy pulse. Then we can compute the direction of ethnic
field distribution and the most. probable points of skirmish between ethnoses;
— one of the ways for ethnic conflict prevention is to fix the territory for certain ethnos. The landscape
features characterized for this ethnos define these territories. So the separation of influence area
of ethnos on territories is realized.
Landscape Delimitation between Ethnoses by Modelling 9
References
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of Social Systems. Omsk: Omsk State University Press.
4, Korobitsin, V.V., and Frolova, J.V. 2002. Simulation of Evolution Dynamics of Social System. Ethnic
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5. Korobitsin, V.V., and Frolova, J.V. 2003. Mathematical Modelling the Ethnic System. Lecture Notes in
Computer Science 2658: 629-635.
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