The Effect Of Two Kinds Of Gaussion Noise To The Dynamical Systems

The chaotic phenomenon widely exists in the nonlinear dynamic system, how to control and use it is a hot topic in today's social studies. Chaos control may have dual function, which is to suppress chaos or to generate chaos. At present, there are two kinds of chaos control, namely feedback control and non-feedback control. The random phase control method, which applied in this paper, belongs to one of the non-feedback control.In this paper, we mainly study the chaos control in the Cords of satellite system, Aviation gyroscope system, Economic crisis system and the Power system. We add the Gaussian white noise and Gaussian color noise in the random phase to implement the control of chaos. The chaotic dynamical behavior is determined by the criterion of the top Lyapunov exponent, which is computed based on the Khasminskii's formulation. When the system is chaotic, the sign of the top Lyapunov exponent is positive. Also when the system is stable, the sign of the top Lyapunov exponent is negative. In addition, Poincarémap, phase portraits and time evolution are studied to further testify the obtained results. It is to show that adding the Gaussian noise in the random phase can suppress chaos or generate chaos.Noise exist widely in real life and the engineering application, also different noise can represent different physical background. We add the different noise to the random phase, its influence to the system is also different. So the work of studying the different noise on the influence of dynamic system has very important realistic application value. The four systems, which discussed in this paper, are widely used in space, economic environment and power system. Therefore the obtained results have not only theoretical value, but also have very important practical value.