The conflict triad dynamical system

Abstract

A dynamical model of the natural conflict triad is investigated. The conflict interacting substances of the triad are: some biological population, a living resource, and a negative factor (e.g., infection diseases). We suppose that each substance is multi-component. The main coexistence phases for substances are established: the equilibrium point (stable state), the local cyclic orbits (attractors), the global periodic oscillating trajectories, and the evolution close to chaotic. The bifurcation points and obvious thresholds between phases are exhibited in the computer simulations.

Dynamical systems of conflict in terms of structural measures

“…where the supremum is taken over all divisions (17) satisfying conditions (18). Then both sequences μN 2 ( Ωs ), ν N 1 ( Ωs ), N = 1, 2, ... converge to zero due to (16) (see the vector version of Theorem 1). Therefore, if the opponent A associated with a measure µ at the first step of the structural approximation looses some region Ω s , i.e., µ ∞ 1 (Ω s ) = 0, then at the second step of structural approximation (under an additional division of Ω s ) using the controlled redistribution inside Ω s it can return a part Ωs of this region.…”

“…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]).…”

“…In [11,15,17,16] we generalized the above constructions to cases of piece-wise uniformly distributed measures, self-similar, and similar structure measures.…”

A Model of Conflict Society with External Influence

“…In this section, we find fixed points of the dynamical conflict system generated by relations (3). They correspond to the vectors p 2 R m 1 whose coordinates do not change under the action of the dynamical system.…”

“…In the present paper, we continue our investigation of the mathematical model of conflict society originated in [1] (see also [2][3][4][5][6][7]). This model describes the redistribution of social energy between individuals of an abstract society under the action of two factors: mutual competition and external influence.…”