Explicitly Solvable Models of Redistribution of the Conflict Space

Abstract

We analyze a class of explicitly solvable models for the problems of redistribution of the conflict space between two alternative opponents. The existence of equilibrium state is proved for a complex nonlinear system whose time evolution is generated by the conflict interaction between its components. Explicit formulas are obtained for the limit compromise distributions in terms of the densities of probability measures. We consider a number of specific model examples of the dynamics of redistribution of the conflict territory and formation of an equilibrium (compromise) distribution of the space. We propose an interpretation of the results for the case of social and territorial conflicts.