Dynamical Analysis Of Third-order Nonlinear Stochastic Systems And Their Control

Stochastic factors are found in engineering science, social science and natural sci-ence widely. There will be a big change in our production and life if we can use or avoid stochastic factors effectively. More and more research scholars focus on the stochas-tic systems. The linear stochastic systems and the second-order nonlinear stochastic systems are studied deeply. There are few people studying the third-order nonlinear stochastic systems. This paper study the dynamics characteristics and chaos control of the third-order nonlinear systems with random parameters by orthogonal polynomial approximation method initially. The main work is as follows:First, stochastic Lorenz system is transformed into its equivalent deterministic one by the second kind Chebyshev polynomial approximation method. By using numerical method we study the dynamics characteristics of this stochastic system and the control of chaotic behaviors based on the time-delayed feedback control method and constant disturbance control method.Second, stochastic Lu system is transformed into its equivalent deterministic one by Legendre polynomial approximation method. According to numerical method we discuss the dynamics characteristics of this stochastic system and the control of chaotic behaviors based on the constant disturbance control method. Furthermore, we investi-gate the strength relationship between control parameters and random parameters when the system is under control.