Study Of Fractional Order IS-LM Macro-Economic Model And Its Complexity

Under the background of "new normal" in the current economic society,our country macroscopically economy is experiencing an unprecedented development transformation and a great opportunity,with the further opening of China's economic environment,and gradually expand the marketization of interest rates,problems and opportunities of China's macro-economy facing are gradually changing.On this basis,this paper analyzes the development situation of China's macro-economy,introduces the corresponding three-dimensional and four-dimensional nonlinear IS-LM economic model according to the theory of chaos and bifurcation theory,and simulates the running state of the macro-economic.Then modifies the nonlinear IS-LM economic model through the modification fractional theory,ensure the "memory characteristics" of economic variables,explores the operation states of fractional order macro-economic system and its complex dynamic characteristics.Conclusions are as follows:1.This paper presents nonlinear IS-LM dynamic evolution model,and described the model in the event of a "liquidity trap" of the specific parameters.In the process of nonlinear analysis and internal complexity of IS-LM model,this paper studies the equilibrium point,the system stability,Hopf bifurcation and other complex dynamics characteristics.In the process of in-depth analysis of the Hopf bifurcation,we introduce the first Lyapunov coefficients innovation,the stability of limit cycle generated with the Hopf bifurcation is studied,and steady state of limit ring are given when the Hopf bifurcation occurs,shows the parameter ranges of the system.2.Through fractional theory,this article constructs a three-dimensional and four-dimensional fractional IS-LM macro-economic model,analyzes the stability of the solution of fractional order systems and its complicated dynamic characteristics.Focuses on the analysis of the Hopf bifurcation condition of fractional order system,shows that the fractional order system can realize the Hopf bifurcation through the changes of the system?s order,which does not affect the relevant economic variables,and has a good application prospect.3.This paper analyses the influence order to the running state of fractional order IS-LM model,analyzes the effect of order on the system state from two perspectives: commensurate order case and incommensurate order case.Analysis shows that,the two kinds of changes will produce similar effects of running state of the system,according to the order of system adjustment,we can guarantee the systems which are chaotic under the integer order condition,can enter into stable convergence condition.4.The effect of parameter variation to the running state in the fractional and integer order system is analyzed innovatively in this paper,research shows that parameter changes can achieve convergence in large range in the fractional order conditions when it is in chaotic state under integer order system conditions,or it can change the economic parameters when the system enter convergence state.This study shows that the fractional theory of analytical ability and good application prospect in the field of economic management,the economic system of fractional order can achieve stable convergence by changing the order number,at this time;some important economic parameter is constant.Therefore,the conclusions of this paper provides a feasible control ideas and methods to carry out the macroeconomic regulation and control in the situation of “new normal",ensure the macro-economic system's operation is stable and health.