Chaos Control Of Several Dynamic Systems By Random Phase

Chaos is one of the most important discoveries in the 20^th century. It is one of the three major revolutions in physics. Chaos control is an important field in explorations of chaos motions, and it is crucial in application of chaos. In this paper, we consider three chaos systems: chaos pendulum system, two-dimensional cellar neural network and the Mathieu equation.At present, there are mainly two sorts of the chaos control's method: feedback control and non-feedback control. In this paper, we control these chaos systems by random phase, it's one of the non-feedback chaos control methods. By adding a random phase we can make chaotic portrait stable. We use Gaussian white noise as the random phase. We can find the chaotic systems dynamical behavior will be suppressed as the noise intensity increases slightly. In this paper, we show that random phase can suppress chaos by the average of the top Lyapunov exponent, which is computed based on Khasminskii's spherical coordinate formulation for linear stochastic systems. In addition, phase portraits, Poincarésurface of section and time evolution are studied to confirm the obtained results. Both methods lead to fully consistent results.In this paper, the three systems have extensive applications, therefore, the results are valuable not only in theory but in project.