Mathematical model of multi-domain interaction based on game theory

Abstract

The article presents a formalised mathematical model of multidomain interaction in hybrid warfare, which covers the cognitive, information, cyber, psychological and physical domains. The object of the study is the nonlinear dynamics of cross-domain destabilisation, which can lead to managerial collapse due to information overload of the control system. The purpose of the study is to identify phase transitions in the management system by analysing domain synergy and coherence degradation. Within the framework of the model based on game theory, the author proposes a matrix of domain reactivity, which determines the strength of mutual influences between domains, and a system of stochastic differential equations with variable coefficients that depend on the emotional state of society, the intensity of information influence and changes in the cognitive background. Two new indicators are introduced for the first time: the coefficient of cognitive penetration and the coefficient of interdomain integration, which allow quantifying the level of cognitive coverage and the degree of synergistic interaction between domains. The introduced parameter of management capacity is used as an indicator of phase shift and system collapse.