The Chaotic Prediction Research Of The Optical Nonlinear System

For a given system, Chaos prediction is to identify whether it has the characteristics of chaos by a certain "observations", it plays an important role in chaos research. The research method can be roughly divided into three categories: First, determine whether the system is with the general characteristics of chaotic motion through the experimental observations; Second, through computer simulation, we obtain the phase diagram and poincarémaps of the system, calculate the Lyapunov index and the Feigenbaum constants. these are belong to the numerical method; Third, analytic prediction which is presented with general conditions of chaos exists by logical deduction of mathematics.In this paper, the development process and trend of chaos,the definition of chaos, chaotic properties, the process of chaotic production are done a a comprehensive overview; the methods of chaos prediction are systematically discussed; We compared all sorts of chaotic analytic prediction method in detail, introduced a new existence theorem for Chaos in the Third-order nonlinear system of autonomy which expands people's understanding of the mechanism of chaos, develops the general theory of the analytical method and is a convenient tool for the practical applications. The numerical methods such as the calculation of Lyapunov index and power spectrum on are studied in-depth.Based on the above, this paper is to do the numerical aspects of chaotic prediction to the typical mathematical model of the optical nonlinear systems------Lorenz system. Based on theoretical analysis,Simulate its way to chaos; Focuse on the system in the (σ,b,r) parameter space the chaotic phenomena of the (b ,r)cross section,the chaotic domain with the changes of the parameters (σ=10,1 < b <9,0