The conflict interaction between two complex systems: cyclic migration

Model of a dynamical system of a conflict triad

“…Taking (3) into account, one can easily verify that inequalities (8) lead to a decrease in the coordinate p i and an increase in r i : As a result, inequalities (8) are replaced by the inequalities…”

“…Note that, in [8], relations (15) were used as certain versions of vector difference analogs of the well-known Lotka-Volterra equations with continuous time. In the present paper, we use discrete time because we assume that the physical continuity does not exist and the mathematical continuity is only a convenient tool of the theory.…”

“…These questions remain open. In [8], we proposed some interpretations of these phenomena. The analysis of other examples shows that a change in one coordinate of the vector P also leads to cyclic oscillations about the initial mean values of coordinates of all three vectors shifted in the direction of increase.…”

“…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].…”

Reconstruction of the spectral type of limiting distributions in dynamical conflict systems

“…Note that, in [13,14] (see also [15]), the composition of conflict is used to construct much more complicated dynamical systems describing, in particular, the processes of migration, social confrontation, and cooperation. In these models, the spectral type of the limiting measures is unstable and can oscillate in the process of evolution repeatedly approaching the singularly continuous and point types (or even the absolutely continuous type).…”