The thesis is devoted to the study and construction of models of discrete dynamic conflict systems with attractive interaction. The notion of dynamic conflict system has appeared as a mathematical tool for describing the behavior of various complex physical systems with two or more conflicting sides. In fact, dynamic conflict system is a system that unites several dynamic systems, whose evolution is deformed under influence of conflict interaction between separate subsystems. Identification of the law of the dynamics of the entire system is a non-trivial task in each specific case; this law must include information about the states of individual components of the system at each moment of time, the type of conflict interaction and its influence on behavior of the system at next moments of time. Even the simplest cases are interesting because of their nonlinearity. The purpose of the theory of dynamic systems of conflict is to give an adequate description of real physical systems, which consist not only of two, but also of many interacting sides.
The purpose of the thesis is to develop the theory of dynamic conflict systems, to build specific models and to study the trajectories behavior in the case when separate subsystems attract each other. In this case, the effect of conflict is that the free opponents behavior is deformed. In particular, they can lose regions of successful presence by concentrating in regions of joint attractors. Finding such limiting attractors, describing their structure, basins of attraction, stationary equilibrium states, the existence of cyclic orbits are typical problems in this research area, which have so far been studied only partially.
The specification of such problems in relation to models of complex dynamic systems with attractive interaction is relevant from the point of view of possible applications in various problems in economics, ecology and sociology. Finding a balance between production and consumption, the use of resources and their natural restoration in the ecological balance, in particular, the search for compromises in contradictory, often acutely conflicting social processes (for example, ethnic, religious, national, linguistic) are not possible without constructing adequate mathematical models of dynamic systems with different types of interactions, both repulsive and attractive.
