Qualitative Analysis Of A Class Of Multiparameter Stochastic Nonlinear Chaotic Systems

Stochastic factors widely exist in many fields, such as natural science, social sci-ence and engineering science. It will bring great changes to human life if we can use or avoid stochastic factors effectively. As a result, more and more scholars are engaged in the research of stochastic nonlinear systems. Compared with ordinary differential equations, stochastic differential equations can more truly and accurately describe the dynamic character of the systems. At present, the second-order nonlinear system with one random parameter is studied deeply. But there are few people studying the high dimensional nonlinear system with multistochasti disturbances and the synchronization between integer-order and stochastic fractional-order nonlinear system. In view of this, the main works are given as follows:1. The high dimensional nonlinear chaotic system with multistochastic distur-bances is investigated. Based on the orthogonal polynomial approximation, the method of transforming the system into an equivalent deterministic system is given. Then dy-namic analysis of the nonlinear chaotic system with multistochastic disturbances can be reduced into that of its equivalent deterministic system. The Lorenz system with mul-tistochastic disturbances is studied to demonstrate the feasibility of the given method. Especially, the influence of stochastic intensity on the system is further studied by the second Chebyshev polynomial.2. The function projective synchronization between integer-order and stochastic fractional-order nonlinear systems is researched. According to the stability theory of fractional-order systems and tracking control, a controller is designed. At the same time, based on the orthogonal polynomial approximation, the method of transforming stochastic error system into an equivalent deterministic system is given. Then the stabil-ity of the equivalent deterministic system is discussed by the proper numerical method. The method is applied to the further study of the function projective synchronization between integer-order Lorenz system and stochastic fractional-order Chen system.