Research On Several Types Of Nonlinear Economic Models And The Application Of Game Theory

Nonlinear phenomena and game behaviors are ubiquitous in nature.Using nonlinear dynamics and game theory to study natural science and social science has become an important research approach.In economics,economic phenomena are usually complicated and unpredictable,so economic systems are usually described by complex nonlinear systems.This paper will present relevant nonlinear models for enterprise competition and economic cycle fluctuation,and analyze its stability,Hopf bifurcation,and so on.In addition,evolutionary game breaks the assumption of completely rational person,and has been widely used in behavior evolution analysis.This paper will use evolutionary game to explore the evolution mechanism of herdsmen’s disaster prevention behavior under the background of climate warming increasing the risk of insect disasters.The main works and innovations of this paper:(1)The influence of government factors on enterprise costs is considered in the discrete enterprise competition model,and then a new continuous three-enterprise competition model with government factors is proposed.The output evolution dynamics of the three-enterprise competition model is studied through theoretical analysis and numerical simulation,and the influence of time delay on the output evolution of enterprises is analyzed in the case of an enterprise bankruptcy.(2)The cooperation factors between enterprises are introduced into the enterprise competition model with adjustment mechanism,and the stability,Hopf bifurcation,and so on of the new enterprise competition model are studied,and the numerical simulation is carried out.(3)The time-delay factor is introduced into the enterprise competition model with cooperation factors and adjustment mechanisms,and then a new enterprise competition model is obtained.Through mathematical analysis and numerical simulation,the influence mechanism of time delay on enterprise output evolution is revealed,and it is found that time delay is an important factor causing economic cycle oscillation.(4)The variable capital stock depreciation rate is introduced into the original Kaldor economic cycle model,and then a new Kaldor economic cycle model is obtained,and its dynamic behaviors are studied.(5)Game theory is applied to the analysis of herders’ disaster prevention behavior and we establish a herder behavior game model with pest feedback under the background of climate warming.By generalizing the specific game model,the game model with population feedback can be obtained.The model combines population dynamics with evolutionary game theory in essence,which is an innovation in evolutionary game research with environmental feedback.By studying the herder behavior game model with pest feedback,the influence mechanism of climate warming on the game system also revealed.