Mathematical and Computer Models of Settlements of Political Conflicts and Problems of Optimization of Resources

Abstract—Nonlinear mathematical models of economic cooperation between two politically (non-military confrontation) mutually opposing sides (two countries or a country and its legal region) are proposed, which consider economic cooperation between parts of the population of the sides, aimed at rapprochement of the sides and peaceful settlement of conflicts. Mathematical models imply that the process of economic cooperation is free of political pressure, that is, the governments of opposing and external sides do not interfere in this process. With some dependencies between constant model coefficients, the first integrals and exact analytical solutions are found. A theorem has been proven to optimize (minimize) the financial resources at which economic cooperation can peacefully resolve political conflict (in the mathematical model we assume that the conflict is resolved if at the same time more than half of the population of both sides support the process of economic cooperation, which promotes political reconciliation). In general, with the variable coefficients of the mathematical model, a computer simulation in the MATLAB software environment was performed to numerically solve the Cauchy problem for a nonlinear dynamic system. Numerical solutions have been obtained, and appropriate graphs have been built. The minimum values of model coefficients (control parameters; optimization of financial resources) under which conflict resolution is possible have been found.