A Learning Model for the Dual Evolution of Human Social Behaviors

M.Nemiche and Rafael Pla López
Department of Applied Mathematics
Universitat de València, Spain
E-mail: Rafael.Pla@uv.es
Web: http://www.uv.es/~pla

Abstract

In this work we modelize, with an abstract mathematical model by computer simulation, the processes that have made to appear in the world a strong duality between orient and occident, by combining changes in conditions of initialisation, natural system and the opposition gregarious/ individualism of the social behaviors.
Finally we present a statistical study of the influence of the repression adaptability, resignation and recycling on the ecological destruction and social evolution.
This model can help us to analyze if the current capitalist globalization can be stopped, changed or regulated, and if it is possible to overcome it toward a Free Scientific Society.

Keywords:  Full repressive society, Free scientific society, Resignation system, Repression system, Science system, Impact system, Historical system, Adaptive system, Natural system

1 Introduction

1.1  We work from a mathematical model of social evolution (Pla-López 1989, Pla-López 1990, Pla-López 1992, Pla-López 1993, Pla-López & V.castellar-Busó 1994, Pla-López 1996b, and V.castellar-Busó & Pla-López 1997 ), to which we call model of Adaptive, Historical, Geographical and multidimensional Evolution with resignation, build from a General Theory of Learning (Pla-López 1988), formulated in terms of the General Theory of Systems. By means of this model Pla-López and Castellar-Busó have studied:
  1. the processes that produce repressive social behaviors in the real world ,
  2. the relationships that provoke these social behaviors among the population's elements,
  3. their influence on the environment and
  4. the necessary conditions to be able to overcome the repression with less repressive and more satisfactory social behaviors.

1.2  This model showed a general social evolution through one only way: in each set of all possible state (dimension) there were an only ideal behavior, which tended univocally to predominate. Thus, there were a correspondence between the successive dimensions and the successive predominant behaviors. Perhaps a dimension were overcome before its ideal behavior arrived to predominate, but it did not alter the linearity of the social evolution.

1.3  Nevertheless, in the real history of the humanity a clear dualism between Orient and Occident appears. If Godelier (Godelier 1970) already showed that the occidental evolution from slavery to capitalism were singular and not general, the experience of the bureaucratic regimens of Orient shows other singularity which cannot be embedded in the Engels’ scheme (Engels 1884), but it have not either been a such ephemeral phenomenon to be explained by our Revolt Effect (Pla-López 1996b). Thus, we have to change our model in order to modelize this dual evolution by using the opposition gregarious/individualism approach and considering the influence of the geographical natural conditions in a new approach on the Natural System

2 Description of the Dualizing Model

2.1  According with the principles of Theory of Learning, each social behavior (U) can change to new behaviors to be adapted to the apparition of new relationships with the other systems and with the common environment. We call Learning to this process that takes place first starting from the own experience of the system and that also can be produced from the knowledge of the experience of the other systems (Learning for diffusion or Scientific Communication). The model is built by means of a Probabilistic Learning, supposing the interaction between a population of NP social subsystems (societies), operated in a common ecological environment and taking a function of fulfillment of its goal
            PG(U,N) = p (U) (1 -s (U,N))
where p(U) indicates a technical possibility of satisfaction of U, and s(U,N) an eventual social repression of U in the individual subsystem N. The better situation is when the technical possibility reaches its maximum value of 1, and there isn't social repression from any N against U (s(U,N) = 0): in this case, the fulfillment of the goal is 1. The social repression can also be adaptable, so that the produced repression tended to approach to the suffered repression. On the other hand, to compare the fulfillment PG(U,N) of the goal with its means value PG(U,N) expresses a personal "resignation" with this mean value: only a fulfillment worse than this mean value provokes rejection. This "resignation" is especially flagrant in flighty situations if the mean value PG(U,N) to compare is updated instantaneously. We can simulate a lower "resignation" through a delay in this updating. Finally, in order to simulate an ecological adaptation, we can introduce a global limit to the natural resources, which can be surpassed if too many resources are simultaneously dedicated to "satisfaction" and "repression". In this case, the system will have to take away resources to recycle, at the expense of the consumption in "satisfaction" or "repression". The possibility of an ecological recovery will depend on the celerity in this adaptation to the ecological necessities.

2.2  We consider a social evolution with discrete time. Each social subsystem N is defined for two variables:
  1. A function of probability P(U,N) on a vector Uº(Um-1,...,U1,U0) of dimension m, with binary components:
    UiÎ{0,1} U = S i 2i Ui. The function P corresponds to the weight of the different social behaviors (state-value) in a social system. The values one or zero of each one of the components represent the presence or absence of some property of the social behavior (also called attribute)
  2. The variable m(N)Î{1,...,m} expresses the native dimension of the system (actual variety of state), which limits the possible behaviors (state) for the restriction:
    P(U,N) = 0 "U ³ 2m(N) when the system is initialised.

2.3  It is necessary to define functions to modelize the level of technological advance, the repressive capacity and the satisfaction of the different social behaviors, also the processes of birth, dead, and relay of the systems. We want that the satisfaction increases with the technological progress. The most simple dependence is f(U) = Si Ui , and if we normalize it we obtain an expression for the technical possibility of initial satisfaction. In a previous work ( Nemiche & Pla-López 2000b), in order to minimize the initial difference in technical possibility of satisfaction between social behaviors, we modelize it with
            p 0(U) = S i¹ 0 Ui / m +(0.8)1-U0 / m
Also, in a previous work (V.castellar-Busó & Pla-López 1997), a new factor had been added to the technical possibility of initial satisfaction to obtain the current technical possibility of satisfaction. This new factor introduces the increase in entropy that is produced through the manipulation of energy and information, by introducing the cost that corresponds to a fraction of the energy that is dissipated and to a portion of the information that is lost. The most developed behaviors are characterised by an upper quantity of transformations of resources in which the energy is dissipated, and by an upper transmission of information, and, therefore, by an upper increase of the entropy. On the other hand, the entropy decreases with the concentration of the behaviors, that is to say, the entropy decreases with the repression. Thus, the technical possibility of satisfaction remains
            p (U) = [1 -ce m (U) / m max(1 -n (U))]p 0(U)
where ce is a parameter which represents the entropy,
            m (U) = S i mi(Ui) = Si 2iUi / (2m -1-1) is the might of U, which will be additive,
            m max = 15 / 7 is the maximum might
and
            1 -n (U) = P i[1 -n i(Ui)] = P i[1- i(1 -Ui) / (m -1)] depends on the ferocity of U, which will be multiplicative.
The initial repressive capacity depends on the might and ferocity of the social behavior,
            k (U) = m (U) n (U); see Table.1

2.4  The core of the model is the Learning System, through positive and negative reinforcement: the probability (P) of each social behavior (U), in each individual subsystem (N) of a social population, is gived by
            P(U,N) = F(U,N) / B(N), such that B(N) = S V F(V,N)
indicates the accumulated memory, and F(U,N) is a memory accumulator function, which increases when the goal is fulfilled and decreases when the goal is not fulfilled from the social behavior U for the individual subsystem N. If no social behavior available to an individual subsystem produces goal fulfilment, then the accumulated memory (B) can become 0 and the individual subsystem is destroyed.
We use a continue approximation by supposing that, through each interval of time Dt, each subsystem has the state-value U and the fulfilment of the goal a number of times proportional to its probability, and therefore
            DF(U,N) = max{-F(U,N), Dt l(N) [PG(U,N) -PR(N)] PL(U,N)}
where PG(U,N) is the fulfilment probability of the goal from the social behavior U for N,
            PL(U,N) is the Learning probability from U for the individual subsystem N,
            PR(N) is a reference value of the satisfaction for the individual subsystem N,
and l (N) is a scale factor for the individual subsystem N.
The fulfilment probability (PG) depends on its technical possibility (p ), which is weighted by a factor determined by the social organisation (1-s).

2.5  This factor is generated by a Repression System: each social behavior, according to its repressive capacity (k), its scope (F ) in each individual system and the impact (imp) of the social behavior , produces a decrease of this factor for the other social behaviors.
Thus, each social behavior (U) represses the other social behaviors, by decreasing its goal fulfilment.
In a previous work (Nemiche & Pla-López 2000b), we modelize the suffered social repression with
            s(U,N) = S V¹ U SM F(V,M) sts(V,M) imp(V,M,N)
where
            sts(U,N) is the repressive capacity of U in an individual subsystem N,
            F (U,N) = P2(U,N) / S
indicates the scope of U in the individual subsystem N, which a number S of active subsystems, and imp(V,M,N) is the impact of the behavior V at the circular distance between the systems M and N.

2.6  Relay System produces a random substitution of an individual subsystem for a "child subsystem" with initial equiprobability of every available social behaviors. A "child subsystem" can also occupy the niche of some destroyed system. Thus, relay causes the loss of the information accumulated in the substituted individual system.
We suppose a generational relay of the individual subsystem N when
            g = a +A(N) +[1 -A(N)] B(N) / tnt³ 1, with a random aÎ[0,1[
where tnt (tanatos) is a lethal value of B(N),
and A(N) indicates the probability of recovery from a destroyed individual subsystem,
such that
            A(N) = a(0) [1 -S U P(U,N)(1 -a(U)) / a(0)],
where a(U) is the probability of recovery when P(U,N) = 1.
In a generational relay, the memory accumulator function F becomes an initial constant value natal, and therefore P(U,N) gives equiprobability for every U <= M(N) = 2m(N) -1, and zero for every U>M(N) (M(N) is the maximum value of U with dimension m(N)), and therefore the Shannon Entropy of the subsystem N reaches its maximum value
             H(N) = -S UP(U,N) log2P(U,N) = log2(M(N) +1),

2.7  Also, a Science System determines the probability of learning (PL) for each social behavior in each subsystem from the probability that the experience of the other subsystems, and which is weighted by factors of emission (EM), reception (RE) and impact (IMP) between individual subsystems, were added to its own experience. This system expresses the relations of intellectual communication between different individual subsystems
If there is not (scientific) communication between different subsystems,
PL(U,N) = P(U,N). In general, if each individual subsystems N has an emission factor EM(N) and a reception factor RE(N),
            PL(U,N) = P(U,N) +RE(N) S M¹ N P(U,M) EM(M) IMP(M,N),
with
            EM(N) = S U P(U,N) em(U), RE(N) = S U P(U,N) re(U),
where em(U), re(U) are the capacity of emission and reception, respectively, from the social behavior U.
Also, capacity of emission and reception will be additive,
            em(U) = S i emi(U), re(U) = S i rei (U)
with emi(Ui) = rei(Ui) = 2i Ui / 15
and IMP(M,N) is a factor of impact between the systems M and N.

2.8  Historical System simulates historical evolution through the random increase of the dimension (m) of the state-variable in each subsystem, and therefore of the number of its available social behaviors. The probability of evolution is increased (b) by the existence of social behaviors, which would be theoretically not available but are forced by System Science from the experience of other subsystems. This system expresses technological progress and technological diffusion (we characterise a technologically higher society by a greater capacity of choice between different social behaviors).
We will simulate historical evolution, through a technological progress, for an increase of dimension of the social behavior.
Thus, we will suppose that the dimension m(N) of the social behavior of an individual subsystem N increases 1 when
            d = b +b(N) +B(N) / prg³ 1 with a random b Î[0,1[
provide that m(N) were smaller than a maxim dimension, prg (progress) is a value of B(N) which compels technological progress, and
            b(N) = S U>M(N) P(U,N)
Provided that in a generational relay (g³1) the memory accumulator function F(U,N) is zero for U>M(N), b(N) can be bigger than 0 only through (scientific) communication. Thus b(N) expresses the diffusion of technological progress.
Moreover, in generational relay (g ³1) with recovery (from B(N) = 0) the newborn subsystem will adopt the dimension of the next "living" individual subsystem (with B(N)>0).

2.9  Adaptive System determines the dynamic evolution of the repressive capacity of a social behavior in a subsystem toward its suffered repression (s ), from an initial value (k ) when it is a "child subsystem",
To express that repressive capacity sts(U,N) of an individual subsystem N is adaptive to it suffered repression s(U,N), we will use a model of systems dynamics, and take
            stst+D t(U,N) = stst(U,N) +Dt [s t(U,N) -stst(U,N)] / Ta
where Ta is the adaptation time of the repressive capacity.
The adaptation time Ta expresses the delay in adaptation of produced repression (sts) to suffered repression (s). Thus, with a low delay Ta, the produced repression equals quickly the suffered repression. On the contrary, with a high delay Ta, produced repression remains approximately constant.
However, in each generational relay (g³1), the value of sts(U,N) will be restored to its initial value. Thus, if adaptation time is bigger than the "middle life" of a subsystem, then a majority of subsystems have values of repressive capacity near of its initial value

2.10  Resignation system expresses the influence of subjective factors through a tendency to a statistical normalisation of the reinforcement from satisfaction and dissatisfaction. We name this tendency "resignation", and express it by a time of delay (Tr) according to a model of systems dynamics: with a low delay Tr, the satisfaction will tend to be compared with its mean value PGM(N), and the individual subsystem tends to be resigned with global low values of satisfaction.
Thus, we express the resignation of the reference value PR and of the scale factor l(N) by means of
                PRt+Dt(N) = PRt(N) +Dt [PGM t(N)-PR t(N)] / Tr
g<1 Þ {
                SRt+Dt(N) = SRt(N) +Dt [SPG t(N) -SRt (N)] / Tr
with initial values
                 PR (N) = PR0(m(N)) = S M(N)³ U p (U) / (M(N)+1)
g³1 Þ {
                SR(N) = SR0(N) = ( S M(N)³ U p (U)2 / (M(N) +1) -PR0(m(N))2)1/2
where
            PGM(N) = S U PG(U,N) PL(U,N) / S U PL(U,N)
is the "mean" of the satisfaction, weighted by the probability of learning,
            SPG(N) = ( S U PG(U,N)2 PL(U/N)/ S U PL(U,N)- PGM(N)2)1/2
is its typical deviation, and
            lt(N) = 2 SR0(N) / SRt(N)
Then, we express the memory accumulator function with
                 Ft+Dt(U,N)=Ft(U,N)+2Dt[PGt(U,N) -PR t(N)] PL t(U/N) SR0(N) / SRt(N)
g<1 Þ {
                or 0 if it is negative.
g ³1 Þ" U£M(N), F(U,N) = natal(N).

2.11  Impact System expresses the influence that has a social subsystem N on another M; we express it by a factor that we call impact (IMP), determined by the function
            IMP(N,M) = S UP(U,N) imp(U,M,N)
where imp(U,M,N) is the impact of the behavior U at the circular distance between the systems M and N.
In the previous works, the impact of a social behavior (imp(U,d)) decreased lineally with the distance, and it is maximum when distance is equal to 0 (d = 0), that is to say, on the own system. This effect only affected to the repression (between different social behaviors).
There are several factors that differentiate the Eastern from the Western social behavior (technical possibility of satisfaction, might, initial repressive capacity...), these differences will also affect their impact: Individualistic in the occidental, and more socially cohesive (Gregarious) in the oriental zone.
Now, we will change the impact function imp(U,d), using the opposition gregariousness/individualism of the social behaviors:
  1. if U0 = 0 (gregarious behaviors), the impact of the social behavior Uº(Um, ...,U1,U0) is maximum when
    d = 0, decreases with d and increases with natal, but
  2. if U0 = 1 (individualist behaviors), the impact is equal to zero when d=0, that is to say, the repression which is produced by such behaviors only acts on other social systems. Thus, the individualist behaviors don't only look for to satisfy its own interest, but rather they make it in such way that abuse to the interests of others.
In the case of NP = 50 we will take
            imp(U,M,N) = exp(-0.5 c2) gre(U,N) ind(U,M,N)
where
            gre(U,N) = [natal(N)(2.3015 exp(-0.5 U2 / 7.25) +U/21)](1 -U0)
            ind(U,M,N) = [c (U exp(-0.5 U2 / 8.064) 6.124 +0.15) / 1.32]U0
where c = d/dis, with dis = (U/2)1-U0 (2U/3)U0.
We can see in Figure.1 some impact functions.
Figure.1 Some impact functions

2.12  Natural System expresses a diversity of initial conditions (natal) of the individual systems. In the previous model, the Natural System appears isolated without input variables.
In this work, we will make that initial conditions (natal) depend on the ecological factor. For that reason, we have included a new factor, to which we call factor of the evolution (km). Then we have changed the definition of the Natural System:
A Natural System determines the dynamic evolution of the initial conditions (natal) of each individual subsystem N, in case of ecological degradation, from an initial value (natal0) toward an ideal value (ntl) with a delay (Tm).
The value initial of natal is
            natal0(N) = natalmin +161d(NP/4,N) / NP,
where natalmin=5
and the value of ntl and natal through the time will be
                ntlt(N) = 2 +( natalt(N) / (-20 ec2 +25)),
ec<1 Þ {
                natalt+D t(N) = natalt(N) +(ntlt(N) - natalt(N)) / km,
where km = Tm / Dt, ec = E/E0
E represents the ecology, and E0 the initial value of the ecology. Through processes of reutilization and recycling, E can increase without overcoming its initial value, and therefore natal(N) can also increase without overcoming the value 2+natal0/5

2.13  Moreover, an Ecological System expresses the degradation of the environment as a consequence of the consumption in satisfaction and repression: the possibility of consumption decreases, so much in satisfaction like in repression, in order to recover the environment by means of the recycling.
The ecology is presented by means of a global variable (E) not negative. This variable will begin from an initial value (E0) enough elevated so that it were possible to kept a consumption or in satisfaction or in repression, during all the evolution (E0 = 2 NP), as high as the whole of the active systems could sustain. Moreover, although the sum of this consumption during all the evolution can amount to the maximal level simultaneously, they won't remain thus by cause of the degradation that the environment would suffer. Thus, this consumption in satisfaction and in repression contributes to the decrease of the resources, and so the variable E decreases and can reach the value zero (Ecological Hecatomb). Also, through processes of reutilization (r) and recycling (r), it is possible the increase of this variable E, without overcoming its initial value E0.
The difference between reutilization and recycling will be that the first didn't include a cost, which will characterize the second. This cost produces a decrease in the consumption in satisfaction, in repression or in both. Each individual system will tend to accept this cost by adapting its recycling to the ecological necessities with a delay Te.
The expression of the consumption in satisfaction, the consumption in repression and the cost of recycling is respectively
            K1 = S N S U [p (U) -r(U,N)] P(U,N)
            K2 = S N S U sts(U,N) P(U,N) and
            K3 = S N S U r(U,N) P(U,N)
The effects of the consumption on the ecology are global, so that the influence on the environment acquires the same form for any social behavior in any system.
The reutilization is associated to natural cycles, so the half of the available resources bound it. We also considered that it is bounded by the consumption in satisfaction and repression and it could not be negative. The expression r = max[0, min[C1E, E0 -E +K1 +K2]] give us the value of the reutilization.
The recycling is formulated concerning an ideal value, which corresponds to the consumed and not reutilized resources and it could not be negative. So, we express the ideal recycling by means of
            rI = max[0, min[E0 -E -r +K1 +K2, E0]].
Finally, we also consider that the maximal possible cost in recycling which corresponds to each social component is bounded by their possibilities of consumption.
So
            r(U,N) = min[p(U), r I / Te(N)] and
            Et+D t = Et +r t+D t +K3t+D t-(K1t +K 2t)
Also, the relationships with the environment modify the satisfaction PG(U/N) for each social behavior in each system, by increasing with the recovery of the environment but decreasing with the cost of the produced recycling, according to
            PG(U,N) = (E/E0) [p(U) -r(U,N)] [1- s(U,N)].

2.14  Finally, a Delay System expresses the decrease of the Adaptation Time Ta with might m and the increase of the Resignation Time Tr with ferocity n, by means of the parameters Ka and Kr respectively. Moreover, Ecological Time Te increases with ferocity and decreases with might by means of a parameter Ke:
            Ta(N) = ka Dt µmax / S U µ(U) P(U,N), where µmax = maximum of µ = 15/7
            Tr(N) = kr Dt [S Un(U) P(U,N) +1] and
            1/Te(N) = [(E0 -E) SUm(U) [1 -n (U)] P(U,N)] / Dt ke E0
where ka, kr, ke are parameters that can vary in a set of initial conditions.
The Figure.2 shows graphically the relationships of our Model

Figure.2 Relationships in the Model

3 A specification of the model

3.1  We work with NP = 50 individual subsystems, and a maximum dimension m = 4
We speak about predominance of a behavior U if its probability is the majority (P>½) in a relative majority of subsystems. Moreover, we speak about strong predominance if additionally its probability of satisfaction (PG) is the maximum.
Table.1 Technical possibility(p0(U)) and initial repressive capacity(k(U))
m
1
1
2
2
3
3
4
4
U
 0º(0,0,0,0) 1º(0,0,0,1) 2º(0,0,1,0) 3º(0,0,1,1) 6º(0,1,1,0) 7º(0,1,1,1) Eº(1,1,1,0) Fº(1,1,1,1)
p0(U)
0.2
0.25
0.45
0.5
0.7
0.75
0.95
1
m(U)
0
0.1429
0.2857
0.4286
0.8571
1
2
2.1429
n(U)
1
1
1
1
1
1
0
0
k(U)
0
0.1429
0.2857
0.4286
0.8571
1
0
0

4 Results and interpretation

4.1  With our Model we have obtained an evolution with behaviors 1-3-7-F ("individualists") in the "occidental" area and 0-2-6-F ("gregarious") in the "oriental" area, which can be explained because in the "oriental" area  natal has a superior initial value (next to 37.5), and so the bigger "gregarious" impact which is generated can compensate the bigger intrinsic satisfactoriness of the "individualistic" behaviors.
A possible interpretation of the dimensions and behaviors would be
  1. Dimension m = 0: Primitive Society
  2. Dimension m = 1: Agricultural Revolution
    Uº(0,0,0,0) = 0: Oriental Empire
    Uº(0,0,0,1) = 1: Occidental Slavery
  3. Dimension m=2: Technological Increase
    Uº(0,0,1,0) = 2: Oriental Feudalism
    Uº(0,0,1,1) = 3: Occidental Feudalism
  4. Dimension m = 3: Industrial Revolution
    Uº(0,1,1,0) = 6: State Socialism
    Uº(0,1,1,1) = 7: Capitalism
  5. Dimension m = 4: Technological Revolution
    Uº(1,1,1,0) = E, Uº(1,1,1,1) = F: Free Scientific Society
Other values of U can represent anomalous social behaviors (Fascism, Stalinism ...) that appear from which we have named "revolt effect". see Figure.6

5 A statistical study

5.1  We have programmed our model in C language, and executed it on the Cray-Silicon Graphics Origin 2000 computer, with 64 processors (MIPS R1200 to 300 MHz), 16 Gbytes by memory central and 390 Gbytes in disk. The operating system is the IRIX 6.5.5, which is a variant of the Unix developed by Silicon Graphics (Servei Informàtic de la Universitat de València).
We have executed our model 3125 times, with (Ka,Kr,Ke)Î{1,4,...,97}x{1,4,...,97}x{1,3,...,9}.
In this paper we limit ourselves our study to the following five evolutions:
  1. Type 1: when appears (predominance) the "2" (Oriental Feudalism) in the "oriental" area and the "3" (Occidental Feudalism) in the "occidental" area.
  2. Type 2: when the oriental and occidental feudalism is overcome with the strong predominance of "7" (Capitalism) in the "occidental" area and "6" (State Socialism) in the "oriental" area.
  3. Type 3: when the Ecological Hecatomb takes place during the strong predominance of the "6" and the "7".
  4. Type 4: when a Capitalist Globalization appears with strong predominance of "7" without to overcome it neither to arrive to an ecological destruction.
  5. Type 5: when the Capitalist Globalization or the duality it is overcome toward a free scientific society "F".
We can see in Figure.3 the five evolutions



Figure.3 Some possible evolutions with duality

In order to study how the previous evolutions depend on ka and kr and ke, we use the REGINT (Caselles 1998) program.

5.2  The proportions p1 to p5 of the evolutions of types respectively 1 to 5 in function of ka are
            p1 = 0.686891 -0.420046 / ka +0.017904 log(ka)
with a correlation coefficient of R = 0.828205
            p2 = -0.056168 -0.000041 ka2 +0.000009 exp(0.1 ka) +0.051254 ka1/2
with a correlation coefficient of R = 0.828643
            p3 =0.015199+0.000003 exp(0.1 ka)+0.005177 exp(-0.1 ka)-0.015602 cos(0.0625 ka)
with a correlation coefficient of R = 0.693814
            p4 = -0.044751 -0.000036 ka2 + 0.000007exp(0.1 ka) +0.043222 ka1/2
with a correlation coefficient of R = 0.831534
            p5 = 0.035582 -0.000003 ka2 -0.091535 / ka +0.06191 exp(-0.1 ka)
with a correlation coefficient of R = 0.83663
In sum, there is a strong correlation of the evolutions 1, 2, 4, and 5 with ka
To find the group of the parameters that facilitate or hind the apparition of the previous evolutions, we show the distributions of the probabilities graphically see Figure.4

Figure.4 Distribution of the probability of ka

We observe that small values of ka facilitate the apparition of the evolution type 5

5.3  On the other hand, the proportions p1 to p5 of the evolutions of types respectively 1 to 5 in function of ke are
            p1 = 4.875047 +0.01956ke2 -1.956964 exp(0.1 ke) -2.271176 exp(-0.1ke)
with a correlation coefficient of R = 0.98772
            p2 = 5.287976 +0.028110ke2 -2.587476 exp(0.1 ke) -2.555235 exp(-0.1 ke)
with a correlation coefficient of R = 0.992130
            p3 = -0.523937 -0.003813ke2 -0.047725 ke+ 0.530948 exp(0.1ke)
with a correlation coefficient of R = 0.914072
            p4 = 3.189116 +0.015755ke2 -1.513678 exp(0.1 ke) -1.544209 exp(-0.1 ke)
with a correlation coefficient of R = 0.75466
            p5 = 0.058542 -0.000441 ke2 -0.052729 / ke +0.017277 cos(0.75 ke)
with a correlation coefficient of R = 0.972099
In sum, there is a strong correlation of the evolutions 1, 2, 3, and 5 with ke

5.4  Finally, the proportions p1 to p5 of the evolutions of types respectively 1 to 5 in function of kr are
            p1 = 0.695407 +0.000006kr2 -0.119897 / kr +0.194476 exp(-0.1 kr)
with a correlation coefficient of R = 0.381090
            p2 = 0.405072 -0.259922 / kr -0.089528 log(kr)+0.015044 ka1/2
with a correlation coefficient of R = 0.602309
            p3 = 0.006503 +0.147729 exp(-0.1 kr)
with a correlation coefficient of R=0.924124
            p4 = -0.090991 +0.000090 kr2 -0.019123 kr -0.000007 exp(0.1 kr)+0.13504 ka1/2
with a correlation coefficient of R = 0.6125882
            p5 = 0.038877 +0.000015 kr2 -0.001066 kr-0.000004 exp(0.1 kr)
with a correlation coefficient of R = 0.47813
In sum, there is a strong correlation of the evolution 3 with kr see Figure.5

Figure.5 Distribution of the probability of kr

We observe that small values of kr facilitate the apparition of the evolution type 3.

6 Conclusions

6.1  We show an interesting result in Figure.6: after of a dual evolution with capitalism in "occidental" zone and state socialism in oriental zone, a globalization of capitalism arrives, but later it is overcome with a Free Scientific Society without Ecological Destruction. Then the current capitalist globalization is an ovecome process.

6.2  No evolution (in the Model) finishes with ecological Hecatomb when the duality is overcame with a capitalist globalization, it is consequence of the decrease of the consumption of the resources in repression and satisfaction.

6.3  According to our model and a first statistical study, with low ka values (quick evolution of the repressive capacity toward the suffered repressive) the probability of the overcoming of the capitalist globalization with a Free Scientific Society increases. This can to explain it for Adaptive Pacifism (disarmament due to a lack of enemies). 
       T=Time, E=Ecology, S=Number of active systems
     T Majority Behavior in the Population(N from 1 to NP) E  S
     0  00000000000000000000000000000000000000000000000000 1.00  1
   100  0000000000-0 -00-00-00-000000000000000000000000000 1.00 49
   200  -0000000 01  1 0100100100 000000000000000000000000 1.00 45
   300  10000000  1  1  10010-10- 00-00-00-000000000000000 1.00 43
   400  1000 -0 - 1  1  1 0101101 00100100100000-000000000 1.00 41
   500  1000 -  1 1  1  1  101101 001-01001000001000000000 1.00 39
   600  100  1  1 -  1  -  1 1101 0011010010000010000000-0 1.00 37
   700  1    1  1 -  1  1  1 11 1 001101001000-0-00000-010 1.00 34
   800  1    1  1    1  1  1 11 - 00110-001000101000001-1  1.00 33
   900  1    1  - - -1  1  1 -1 1  01101001-001010000-11-  1.00 33
  1000  1    1  1 1 11  -  1 11 1   -10100110-101-0001111  1.00 32
  1100  1    1  1 1 11  1  1 11 1   1- 100110110110001111  1.00 31
  1200  1    1  1 1 11 -1  1 11 1   11 1 011-110110  1111  1.00 29
  1300  1    -  1 1 11 11  1 11 1-  11 -  111-1011   1111  1.00 28
  1400  1    1  1 1 11 11  1 11 11  -1 -  11111 11   1111  1.00 27
  1500  1    1- 1 1 -1 11  1 11 11  11 1  11111 11   1111  1.00 28
  1600  1    11 1 1-11 11  1 11 11  11 1  -1111 11-  1111- 1.00 30
  1700  1-   -1 - 1111 11  1 11 11  11 1  11111 111  1111- 1.00 32
  1800  11   11 1 1111 -1  1 11 11  11 1  11-11 111  1-1-1 1.00 32
  1900  -1   11 1 1111 11  1 11 11  -1-1  11111 111  1-111 1.00 33
  2000  11   1- 1 1111 11  1 11 11  1-11  11111-111  1-111 1.00 34
  2100  11   1--1 11-- 11  - 11 -1  --11  11-111111  1-111 1.00 35
  2200  11   1111 1111 11  1 1- 11  1111  111111-11  1-111 1.00 35
  2300  11   1111 11-1 11  1 -1 11  1111  1111-1111  1-111 1.00 35
  2400  11   1111-1111-11  1 11 11  1111  111111111 -1-111 1.00 38
  2500  1- - 111111-11111  1 11 11  11-1  111111111 11-111 1.00 39
  2600  11 - 111111-11111  1 11 1-  1111  11111-11- 11-111 1.00 39
  2700  11 - 111-1111111-  1 11 11  1111  11111111- 11--11 1.00 39
  2800  11 - 111111111111  1 11 1-  1111  1111-1111 11--11 1.00 39
  2900  11 - 111111111111- 1 11 11  1111- 111111111 11--11 1.00 41
  3000  1- - -11111111111- 1 11 11  11111 -11111111 1---11 1.00 41
  3100  11 - -11111111111- 1 11 11  11111 111111111 1---11 1.00 41
  3200  11 ---11-111111111 1-11-11  11111 11-1111-1 11--11 1.00 44
  3300  11 3--111111111111 1111111  11111 1-11111-1 11--11 1.00 44
  3400  11 3-31-1111111111 1111-11  111-- 1111111-1 11---1 1.00 44
  3500  11 3--1-1111111111 1111-11- 11-11 11111-1-1 ----31 1.00 45
  3600  1- 33--31111111111 111111-1 11111 1-1-111-1 ----31 1.00 45
  3700  -3 33-3311111-11-1 11111111 -1111 1-1--1--- ----3- 1.00 45
  3800  -3 3-3333111111111 111-1111 -1111 1-1------ --2-3- 1.00 45
  3900  -3 3--333111111111 11111111 11111 111------ --2-3- 1.00 45
  4000  -3 3--3-33-1111-11 111-1111 1-111 1-1------ --223- 1.00 45
  4100  -3 3333--311111111 111111-1 11111 1-----------223- 1.00 46
  4200  -3 3333--3--111111 11-11111 11111 1-----------2233 1.00 46
  4300  -- 3333--333111111 11111-11 1111- 1----------22233 1.00 46
  4400  -- --33--3331111-1 11111-11 1-111 -----------22233 1.00 46
  4500  -- --3--3-33-11111 11111-11 1111- -----------222-- 1.00 46
  4600  -- --3----33331111 11111-11 1-1-- -------7---2222- 1.00 46
  4700  -- ----7--3333-311 11111-11 1-1-- ---6---7---222-- 1.00 46
  4800  -- ----7-7-3-3---1 11111-11 1---- ---6----6--222-- 1.00 46
  4900  -- ---77-7-------1 -1111--- 1---- ---66-66---22--- 1.00 46
  5000  -- ----7-7------7- -1111--1 1---- ---66-66---22--- 1.00 46
  5100  -- ----777------77 7-111--1 ----- --66-666-6222--- 1.00 46
  5200  -7 -7--777-----777 77-1---- ----- -666-666-6222--- 1.00 46
  5300  -7 -777777---7-7-7-7777---- ----- 6--6-666-6222 -- 0.99 46
  5400  -7 77777777-77---7-7777---- --666 6--6-66666222 -7 0.95 46
  5500  -7 77777777-777--7-77777-7- -6666 6--6--6666222 -7 0.87 46
  5600  -7 77777777-77777777777777- -6666 6-66--6666222 -7 0.77 46
  5700  -7 7--77777-77-7777--77777- -6666 666---6666222 -7 0.65 46
  5800  -7 7--77777--7-7777--77777- -6666 666-6-6666-22 -7 0.54 46
  5900  -7 -  77777  7 F-77  777777--6-66 6-6- -6-66-22 -7 0.44 39
  6000  -7 -  77777  7   77  7777-7-66-66 6-6   6-66 22 -7 0.41 34
  6100  -7    77777      77  -777---6- 66 6     6-66 22  7 0.41 28
  6200  -7    77777      -7  -777  -6- 66 6     6 66 22  - 0.46 25
  6300  F7    77-77           -77  -6  66 6     6  6 22  - 0.57 20
  6400   7    77-77           -77   6  66 6     6  6 -2    0.73 18
  6500   7    -7 77            77   6  66 6     6  6 -2    0.96 15
  6600   7    -7 77            -7   -  66 6     6  6 72    1.00 15
  6700   7    77 77            -7   -  66 6     6  6 72    1.00 15
  6800   7    77 77            -7   -  66 6     6  6 72    1.00 15
  6900   7    77 77            -7   -  66 6     6  6 72    1.00 15
  7000   7    77 77            -7   -  66-6  -  -  6 72    1.00 17
  7100   7    77 77            -7   -  66-6  -  -  6-72    1.00 18
  7200   7    77 77      -     -7   -  66-6  -  -  6-72    1.00 19
  7300   7    77 77      -     77   -  66-6  -  -  6-72    1.00 19
  7400   7    77 77      -     77   -  66-6  -  -  6--2    1.00 19
  7500   7    77 77      7     77   -  66-6  -  -  67-2    1.00 19
  7600   7    77 77      7     77   7  6-66  -  -  6772    1.00 19
  7700   -    7- 77      7     77   7  6-66  -  -  -772    1.00 19
  7800   --   7- 77      7     77   7  6-66  -  -  -772    1.00 20
  7900   7-   -7 77      7     7-   7  6-66  -  -  -77-    1.00 20
  8000   7-   -7 7-      7     7-   7  6--6  -  -  -77-    1.00 20
  8100   7-   77 7-      7     7-   7  6--6  -  -  -77-    1.00 20
  8200   7-   77 77      7     --   7  6--6  -  -  -77-    1.00 20
  8300   7-   77 77      7     --   7  6---  -  -  7777    1.00 20
  8400   7-   77 77      7     --   7  6---  -  7  7777    1.00 20
  8500   7-   77 77      7     -7   7  ----  -  7  7777    1.00 20
  8600   7-   77 77      7     -7   -  ----  -  7  7777    1.00 20
  8700   7-   77 77      7     -7   -  ----  -  7  7777    1.00 20
  8800   7-   77 77      7     77   -  ----  -  7  77-7    1.00 20
  8900   77   77 77      7     77   -  ----  -  7  77-7    1.00 20
  9000   77   77 77      7     77   -  ----  -  7  7--7    1.00 20
  9100   77   77 77      7     77   -  ---7  -  7  7-77    1.00 20
  9200   77   77 77      7     77   -  ---7  -  7  7-77    1.00 20
  9300   77   77 77      7     77   -  ---7  -  7  7-77    1.00 20
  9400   77   77 -7      7     77   -  ---7  -  7  7-77    1.00 20
  9500   77   77 -7      7     77   -  ---7  -  7  7-77    1.00 20
  9600   77   77 77      7     77   -  ---7  7  7  7-77    1.00 20
  9700   77   77 77      7     77   -  ---7  -  7- 7777    1.00 21
  9800   -7   77 77      7     77   -  ---7  -  7- 7777    1.00 21
  9900   -7   77 77      7     77   -  ---7  -  7- 777-    1.00 21
 10000   77   77 77      7     77   -  ---7  -  7- 777-    1.00 21
 10100   7-   77 77      7     77   -  ---7  -  7- 777-    1.00 21
 10200   7-   77 77      -     77   -  ---7  -  7- 7777    1.00 21
 10300   7-   77 77      -     77   -  ---7  -  7- -777    1.00 21
 10400   7-   77 77      -     77   -  ---7  -  7- -777    1.00 21
 10500   7-   -7 77      -     77   -  ---7  -  7- -777    1.00 21
 10600   7-   -7 77      -     --   -  ---7  -  7- -777    1.00 21
 10700   7-   -7 77      -     --   -  ----  -  7- -777    1.00 21
 10800   7-   77 77      -     --   -  ----  -  7- -777    1.00 21
 10900   7-   77 77      -     --   -  ----  -  7- -777    1.00 21
 11000   7-   77 77      -     --   -  ----  -  7- -777    1.00 21
 11100   7-   77 77      -     --   -  ----  -  7- -777    1.00 21
 11200   7-   77 77      -     --   -  ----  -  7- -777    1.00 21
 11300   7-   77 77      -     --   -  ---- --  7- -777-   1.00 22
 11400   7-   77 77      -     --   -  ---- --  7- -777-   1.00 23
 11500   7-   77 77      -     --   -  ---- --  7- -777-   1.00 23
 11600   7-   77 77      -     --   -  ---- --  7- -777-   1.00 23
 11700   7-   -7 77      -     --   -  ---- --  7- -77--   1.00 23
 11800   7-   -7 77      -     --   -  ---- --  7- -77--   1.00 23
 11900   7-   -7 77      -     --   -  ---- --  7- --7--   1.00 23
 12000   7-   -7 77      -     --   -  ---- --  -- --7--   1.00 23
 12100   7-   -7 77      -     --   -  ---- --  -- --7--   1.00 23
 12200   7-   -7 77      -     --   -  ---- --  -- --7--   1.00 23
 12300   7-   -7 77      -     --   F  ---- --  -- --7--   1.00 23
 12400   7-   -7 77      -     F-   F  ---- --  -- --7--   1.00 23
 12500   7-   -- 77      -     F- - F  ---- --  -- -----   1.00 24
 12600   --   -- 77      -     FF - F  F--- --  -- -----   1.00 24
 12700   --   -- -7      -     FF - F  FF-- --  -- -----   1.00 24
 12800   --   -- -7      -     FF - F  FF-- --  -- -----   1.00 24
 12900   --   -- -7      -     FF - F  FF-F --  F- F----   1.00 24
 13000   --   -- -7      F     FF F F  FF-F --  F- F----   1.00 24
 13100   --   -F -7      F     FF F F  FF-F F-  F- F----   1.00 24
 13200   F-   -F -7      -     FF F F  FF-F FF  FF F----   1.00 24
 13300   F-   -F -7      -     FF F F  FF-F FF  FF F----   1.00 24
 13400   F-   -F F7      -     FF F F  FF-F FF  FF F-FF-   1.00 24
 13500   F-   -F F7      F     FF F F  FF-- FF  FF F-FF-   1.00 24
 13600   F-   -F F7      F     FF F F  FF-- FF  F- FFFF-   1.00 24
 13700   F-   -F F-      F     FF F F  FF-- FF  F- FFFF-   1.00 24
 13800   F-   FF F-      F     FF F F  FF-F FF  F- FFFF-   1.00 24
 13900   F-   FF FF      F     FF F F  FF-F -F  F- FFFF-   1.00 24
 14000   F-   FF FF      F     FF F F  FF-F -F  FF FFFF-   1.00 24
 14100   F-   FF FF      F     FF F F  FF-F -F  FF -FFF-   1.00 24
 14200   F-   FF FF      F     FF F F  F--F -F  FF -FFF-   1.00 24
 14300   F-   FF FF      F     FF F F  F--F -F  -F -FFF-   1.00 24
 14400   F-   FF FF      F     FF F F  FFFF FF  -F FFFFF   1.00 24
 14500   F-   FF FF      F     FF F F  FFFF FF  FF FFFF-   1.00 24
 14600   FF   FF FF      F     FF F -  FFFF FF  FF FFFF-   1.00 24
 14700   FF   FF FF      F     FF F -  FFFF FF  FF FFFF-   1.00 24
 14800   FF   FF FF      F     FF F F  FFFF FF  FF FFF--   1.00 24
 14900   FF   FF FF      F     FF - F  FFFF FF  FF FFF--   1.00 24
 15000   FF   FF FF      F     FF - F  FF-F FF  FF FFFF-   1.00 24

Figure.6 An example of dual evolution from the model

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