Nonlinear Stochastic Parameter System Dynamics And Control Research

Bifurcations, chaos and its control in the stochastic nonlinear dynamical systems with random parameter are investigated in this paper. The main contents of this paper are as follows:In chapter one, the researching background of nonlinear dynamics is mentioned. After that, the development history and the current developments of stochastic nonlinear dynamical system with random parameter are introduced here. Finally, there shows the researching methods and the main contents of this paper.In chapter two, the dynamical behaviors of the stochastic double-period bifurcation and the stochastic Hopf bifurcation in the stochastic Bonhoeffer-van der Pol system are researched by the Chebyshev orthogonal polynomial approximation method, which firstly reduces the stochastic nonlinear dynamical system into its equal deterministic nonlinear dynamical system, then getting the results by using the effective numerical method to this equal system. The numerical results show that the stochastic bifurcations in the stochastic Bonhoeffer-van der Pol system are by and large similar to that in the deterministic Bonhoeffer-van der Pol system. But with the effect of the random factor, there are still some featuring differences between them. Meanwhile, the obtained results show that Chebyshev polynomial approximation is an effective approach to dynamical problems in some typical nonlinear systems with bounded random parameter of an arch-like probability density function.In the chapter three, using the same equal deterministic system in the chapter two, the stochastic chaos in the stochastic system with the random parameter is studied. The numerical results show that the chaos behavior in the stochastic Bonhoeffer-van der Pol system is by and large similar to that in the deterministic Bonhoeffer-van der Pol system. Afterward, the chaotic behaviors are controlled by both noise which is non-feedback control method and time-delay feedback control method. Because of the random factor, there are some futures in the analysis and controlling of chaos.In the chapter four, the chaos behaviors the in Duffing-van der Pol system are discussed, and the controlling of chaos by noise are researched too.In the last chapter, the conclusions of the whole paper and the points for the further researches in the field of the stochastic nonlinear dynamical system with the random parameter are given.