Dynamics of conflict interaction between systems with internal structure

Abstract

We investigate a dynamical system of conflict between two systems each of which, in turn, has an internal conflict. The external conflict and the internal one have different natures. The external conflict is described by an alternative interaction between nonannihilating adversaries. The internal conflict is similar to a conflict between interrelated populations of different biological nature ("predator-prey" model). We construct a computer model of this system and describe a typical behavior, illustrated by diagrams, which can be interpreted, in particular, as a migration of labor and investments between countries.

Dynamical systems of conflict in terms of structural measures

“…If Ω is a finite set and µ, ν are stochastic vectors p, r ∈ R n +,1 , then coordinates of the limit states {p ∞ , r ∞ } are described by (5). We refer to [12,13,18]) for the proof of this theorem.…”

“…We study the emergence of space redistributions arising due to the conflict interaction between opponents (opposite sides, players). The roles of opponents may be played by various natural entities with alternative trends (for examples see [5,7,9,11]). In turn, the conflicting space may appear as a territory, a living resource, an ordering queue, in general, any value admitting division (see [2,6,10,16,21]).…”

“…Let us explain our approach in more details (see also [1,4,5,11]- [15], [20]). Denote by A, B a couple of opponents (alternative sides) living on a common resource space Ω.…”

The conflict triad dynamical system

“…For the proof see [12,13] and [14,15,2,3,7]. We remark that in [2] the formulae (2.15) was used for the construction of complex system which generalize the well-known predator-prey model and is in fact some variant of the vector analog of Lotka-Volterra equations.…”

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).…”