Research of a nonlinear dynamic system describing the mathematical model of the bipolar world

‎Over the past few decades‎, ‎mathematical modeling of social processes‎, ‎such as information warfare‎, ‎language globalization‎, ‎ethnic assimilation‎, ‎political conflicts‎, ‎the process of state territorial stability‎, ‎etc‎. ‎has been of particular interest‎. ‎Currently‎, ‎the ongoing military events related to the Russian invasion of Ukraine are directly Russia’s desire to change the natural course of geopolitical influence distribution on the world policy of the two main powers USA and China‎, ‎where the their economic components in world GDP (Gross Domestic Product) are respectively 28.78\% and 18.53\%‎. ‎For comparison‎, ‎Russia's contribution to world GDP is 2.54\%‎. ‎This paper proposes new nonlinear mathematical models describing both a bipolar (USA‎, ‎China) system of real influence on world politics‎. ‎Mathematical models are described by two‎- ‎dimensional nonlinear dynamic systems with variable coefficients and corresponding initial conditions characterizing the current state of influence of the world’s main actors‎. ‎The models consider the conditions for rationing solutions‎, ‎which imply a complete redistribution of world influence in case of a bipolar world between the United States and China‎, ‎and the contribution of other countries is considered insignificant‎. ‎In the mathematical model of the bipolar arrangement of the world‎, ‎exact analytical solutions are obtained in quadratures‎, ‎showing the dynamics of changes in the influence of these two powers on world politics‎, ‎i.e.‎, ‎changes in their relative contribution to the redistribution of world influence‎. ‎At some values of the variable coefficients of the mathematical model‎, ‎accurate periodic solutions of the dynamic system were found‎, ‎describing the process of alternating dominance of the political weight of the United States and China‎.