Research Of The Phase Space Reconstruction Of Dynamical Systems And Its Practical Verifying Analysis

Symbolic dynamics has a lot of theoretical and practical applications. It's not only an important research object, but also a powerful research tool, which is shown in this paper. In chapter 1 basic knowledge of chaotic dynamics is introduced, and then symbolic dynamics method is employed to discusse the chaotic properties of several dynamical systems in chapter 2.A real physical system may involve many variables but only one or more of them can be detected by modem data collecting equipment In recent years, the technique of phase space reconstruction is frequently applied to analyse and process time series. Its significance is that the topological characteristics such as fractal dimension can be obtained, On the basis of investigation and research about the technique of phase space reconstruction up-to-now, this paper is also devoted to develop a new method for the prombles of detecting deterministic chaos of time series obtained from experimental data.As an example, the time series of China composite stock index is considered Firstly, the distribution of five day's return on China composite stock index is studied. Secondly, based on the R/S analysis Hurst exponent is worked out and determination detecting can be done . Lastly, the topological characteristics such as correlation dimension and maximum Lyapunov exponent are extracted from time series.