Dynamic Analysis Of Solow Model With Environment Purification

Economic growth has been one of the hot issues of macroeconomic research.However,with the rapid growth of economy,environmental pollution even deterioration has been a serious threat to the development of human society.So,it is urgently to solve the problem about how to realize the coordinated development of economy and environment.Considering economy-environment system is a complex and nonlinear system,in order to analyze the system,based on the Solow model with environment purification,the paper introduces double random parameters,fractional order term and double time delay parameters respectively,then Solow model with double random parameters,fractional order Solow model and Solow model with double time delay parameters are put forward for the first time.Nonlinear dynamics theory is utilized,and numerical simulation and parameter analysis are implemented to study the dynamic behavior of the Solow model,which further reveals the law of dynamic evolution of the economy-environment system.Result shows that economy-environment system is greatly influenced by environmental purification ability and the relative change rate of labor force,that the greater of the two parameters’ random strengths,the smaller the coordinated development regional of economy-environment system;fractional order Solow model has so high sensitivity to some parameters that bifurcation happened near the critical parameters,then the limit cycle phenomenon happened namely economic cycle;the increased pollution abatement investment has some deterrent effect on economic recession;fractional order model has more advantages than integer order model in describing the economic environment system;the Solow model with double time delay parameters has so high sensitivity to investment delay parameters that the economic cycle will be triggered by individual investment delay or two delay,and with the increasing of the time delay,economic cycle fluctuation will become more intense.All the above says that the stable operation of the economy-environment system can be realized by controlling the random strength of random factors and adjusting the investment policy to meet the expected balance target.