Stochastic Dynamical Behavior Analysis Of A Kind Of Economic Model

With the continuous development of the global economic,various factors affect the operation of the economics,and these factors are very complex.The traditional economic theory is unable to describe it accurately.Nonlinear economic theory gradually becomes the research trend of contemporary economic,and it provides new research ideas and methods for current state of the complex economic operation.In this paper,on the basis of the theory of modern nonlinear dynamics theory and stochastic dynamics,the complex nonlinear phenomena of the economic system is researched,and the internal influence of uncertain factors are analyzed.In this paper,the mainly studies are as follows:Firstly,this paper introduces the development of present situation of the economic system,as well as the current research status of stochastic dynamics theory.The theory analysis method,stability and dynamic behavior of nonlinear dynamic system are introduced in this paperSecondly,the Chebyshev orthogonal polynomial approximation method is applied to investigate the Hopf bifurcation problem of stochastic economic system with bounded random parameters.The stochastic system is reduced to its equivalent deterministic one.Then the Hopf bifurcation condition of the system is obtained,and we verified the validity of these results by numerical simulations.Numerical results show that the economic system has complex nonlinear dynamic characteristics with the influence of random factors,we also know the increase of random strength ? not only makes the system bifurcation value shift to left,but also inhibit the increase of the limit cycle amplitude.Thirdly,the inherent complexity of a class of nonlinear economic period model with harmonic random noise excitation is studied.The Lyapunov direct method is used to study the stability of the zero solution of the system without disturbance.We find that the system is asymptotically stable near the zero solution.Using the multiple scale method to solve the first-order approximate solution of the equation.The relationship between small quantity of excitation frequency and the the first orderapproximate solution amplitude is discussed.And we obtain the change of system parameters on the influence of response amplitude is very significant.Finally,we give the brief conclusions,including the main content,innovation points and the follow-up work.