Theorem on Conflict for a Pair of Stochastic Vectors

Model of a dynamical system of a conflict triad

“…Note that the mathematical model of the conflict triad is based on the notion of the dynamical conflict system introduced in [4][5][6][7][8][9]12]. Among other deep theoretical investigations that influenced our constructions, we mention the results of [14][15][16][17][18][19][20].…”

Properties of the Limit States of a Dynamical Conflict System

“…In the case of finitely many conflict positions, we have p, r ∈ R n , n < ∞. If the number of conflict positions is arbitrary, then we assume that p, r ∈ l 1 . The values of the coordinates p i and r i are interpreted as the independent probabilities of occupying the ith conflict position by the corresponding opponents.…”

“…The notion of conflict composition for stochastic vectors with a finite number of coordinates and the coupling coefficient α = 1 was first introduced in [1] (see also [2,3]). In the present paper, the notion of conflict composition for indestructible opponents with repulsion effect is generalized to the case of an arbitrary value of the coupling coefficient 0 < α ≤ 1.…”

“…In the case α = 1, the conflict composition is well defined if the initial vectors satisfy the condition 1 = (p, r). It should be noted that the value of p (1) i is proportional to the product of the initial probability p i of occupying the ith position and the probability of the absence of the opponent at this position (the last quantity is taken with regard for the coefficient of interaction α). The quantity r (1) i is interpreted by analogy.…”

Segregation through Conflict

“…One case is that there are two rows, It must be emphasized that the limiting distribution of the matrix strongly depends on the initial conditions. Koshmanenko shows such phenomena in a purely mathematical way for two opponents (Koshmanenko, 2003(Koshmanenko, , 2004. However in the next section they are demonstrated through a generalized simulation so that more complicated situations may be dealt with.…”