Based On Chaotic Time Series Phase Space Reconstruction

Based on a one-dimensional chaotic time series phase space reconstruction related to delay time and embedding dimension determination. Determining the delay time is an important step for chaotic analysis, which will directly affect the determination of reconstruction attractors. At present, there are three methods to select delay time: self-correlation function method; the average displacement method and mutual information method.The equal-probability symbolic analysis approach of calculating the mutual information function is proposed to improve the incorrect value caused by routine symbolic analysis method. Firstly, the time series are rearranged according to range from small to large. Then the rearranged time series are divided into several groups by equal-probability step and the number of groups are determined by computing empirical sub-formula. Finally, a critical point set of symbolic analysis method is composed of boundary values of each group. The results of the experiments of Lorenz and forced Brusselator show that this approach agrees well with Fraser' method while the algorithm is simplified significantly.Embedding dimension is also an important parameter in phase-space reconstruction. this paper describes several typical embedding dimension algorithm, and conducts simulation experiments of Lorenz system in conditional entropy method. The result of experiment show that this approach is reasonable.Finally, this paper introduced several calculating the maximum Lyapunov index and the correlation dimension methods. the same simulation experiment of the Lorenz system was conducted and the Lyapunov index and the correlation dimension we calculated are basically consistent with the theoretical values, the result show the rationality of calculation of the best time delay and embedding dimension of the Lorenz system in this paper.