Chaos Control Problem

In the second half of the twentieth century, nonlinear science has achieved an unprecedented development, which concerns the basic problems, such as the logic systems and innovation of modern science, and influenced the people's way of thinking deeply. Generally speaking, the majority of nonlinear science includes the researches of chaos, fractal, soliton and complexity, among which the research of chaos plays a much larger part than others.In this paper, the research ways of nonlinear problems have been introduced, which includes analytic method, phase-space method and numerical method. Furthermore, we introduced the basic theory about chaos, concerning the definition of chaos, the features of chaos movement, the research methods of chaos, and the control and synchronization of chaos, etc. Based on these theories, the following problems have been investigated:1. The chaos occurring in Josephson junctionsThe Josephson junctions have a great potency of development in the practical applications. But, with the increases of gain, the abnormal noise rises in Josephson junction parametric amplifiers. Later it was found that the noise was caused by the chaos existing in it. In addition, in the SQUID made of Josephson junctions, the phenomenon of chaos has also been found. In this paper, chaos occurring in Josephson junctions is investigated by phase-space and numerical methods. Moreover, the stability of Josephson junction system has been discussed. The results will lay a more reliable theory basis for the high performance superconductive devices based on Josephson effects. All of the numerical analysis is based on the Runge-Kutta method of 4,5 step algorithm, the algorithm can guarantee a certain accuracy, but without affecting the temporal complication and spatial complication in computations.2. The analysis of prospect of the application of Rossler Lorenz and Chen's chaotic attractors in secure communicationIn 1999, Chen guan rong, the professor of Houston University in American found a new attractor, which is now known as Chen's attractor. In this paper, simulation experiments have been worked with EWB and the chaotic waves of the Rossler, Lorenz and Chen's attractors are investigated. It is very evident that the chaotic waves of Chen's attractor are more complex. Moreover, the synchronization of Chen's system has been confirmed. Based on these we come to a conclusion that Chen'sattractor would have a greater potential in the application of information encryption and secure communication.