Research On Dynamic Behavior Of Nonlinear Economic Model

Fluctuation is an economic trend characteristic in any economic form,and researching its theory can provide important reference information for the discussion of economic fluctuation mechanism and the forecast of economic development prospect.Hence,the investigation of economic fluctuation has been paid much attention by economists.Since established the classical business cycle model,the linear econometric model has gradually become a mainstream model to investigate economic fluctuations.In recent years,with the development of nonlinear methods,the nonlinear characteristics of the economic system have been confirmed,and they are widely attracting attention.However,the existed nonlinear economic model is still relatively simple,and it is worth discussing for the dynamic behavior of the nonlinear economic system.Based on the above,by combining the Goodwin consumption function and the Puu investment function,we establish some new nonlinear economic models and analyze the dynamic behaviors of bifurcation,the first passage time etc of them.In this dissertation,the main works are as follows:1.Investigating the stability and bifurcation of the new business cycle models to explore the mechanism of the economic fluctuation.Firstly,using the Goodwin consumption function and the Puu investment function and combining with the historical data of China's macro-economy,we establish the new deterministic model,periodic noise excitation model and stochastic noise excitation model,respectively.Secondly,according to the stochastic averaging method and the unified colored noise principle,the stability and bifurcation of business cycle models are studied by the maximum Lyapunov exponent and the stationary probability density function of the system response.Finally,the different models are compared and analyzed to explore the similarities and differences between them.The results show that the marginal rate of consumption has a significant impact on the stability and bifurcation of those business cycle models.The change of the noise intensity will lead the business cycle model with periodical noise into chaotic state.Compared with the deterministic economic model,the dynamic behavior of the stochastic model is more complicate.With the change of the marginal consumption rate,noise intensity and the autocorrelation time of the noise,the numerical results show that there exist period doubling D-bifurcation and multiple P-bifurcation for the business cycle model under colored noise excitation.2.The first passage problem of the business cycle model with colored noise is discussed in detail to show the evolution law of reliability of business cycle model.Firstly,the boundary type of the model is determined by the boundary classification method of one-dimensional diffusion process.Secondly,the reliability density function and the first passage time are obtained by BK equation,GP equation and the reliability function.Finally,the following conclusions are deduced from numerical simulation: In the case of fixed noise autocorrelation time and noise intensity,the reliability function,the reliability density function and the first passage time are not monotonic functions of marginal consumption rate;the reliability of business cycle model present the phenomenon of fluctuation with increasing of marginal consumption rate.3.By researching the stability and bifurcation of nonlinear foreign investment economic model to analysis the influence of foreign investment on economic model.Firstly,based on the Puu-Goodwin business cycle model,we constructed the unilateral and bilateral foreign investment economic models,respectively.Secondly,the stability of the foreign investment economic model is studied by the characteristic root method.Finally,under non-resonance and internal resonance,the P-bifurcation condition of the stochastic model is analyzed,respectively.The results show that the growth stability of the economic system has been obviously affected by the economic level and the external excited noise.For the relatively small economic level difference between two countries,there are relatively stable benefits of both sides in the foreign investment activities;otherwise,it trends to instability.Through analyzing unilateral and bilateral foreign investment model,we can find that the bilateral foreign investment model is more conducive to the steady economic development of countries in foreign investment activities.But the stability of investors' economic development is impacted by invested party for the unilateral foreign investment model.4.We investigate the stability influence for evolutionary game model of bilateral foreign investment through discussing its relationship with agreement and cooperation.On the one hand,analyzing the condition of symbolic of the replicator dynamic equation,we deduce the stability decision of each player.On the other hand,by analyzing the determinant and trace of the matrix of bilateral foreign investment evolutionary game model,we obtain the stability of game group decision making.The results show that,under expectation of mutually beneficial cooperation,both game players will enter the "cooperation" evolutionary state independent of the initial conditions.Reasonable investment cooperation agreement can restrain the behavior of both investors,and then,it plays a decisive role in the final evolution of investment process.