Study On Distributional Chaos Theory And Prediction Technology Of Chaotic Time Series

The study of dynamical properties of the general symbolic dynamical system is a very importent problem.In the tens of years'fast development of symbol dynamic,under the efforts of the numerous mathematics workers,many pretty important theoretical and realistic results have been reached.In order to reveal inner link between Li-Yorke chaos and distributional chaos in a sequence,Du Fengzhi,Wang Lidong and Ge Yunying give the notion of distributional chaos in a sequence,and they also point out that a continuous map of a interval is Li-York chaotic if and only if it is distributionally chaotic in a sequence.But Liao Gongfu and Fan Qinjie point out that Li-Yorke chaos is equivalent to distributional chaos on their restricted measure centers.We study the relation among the distributional chaos,distributional chaos in a sequence and{P_i}*—chaos then reach some importent results.Chaos is a irregular behaviour which is a wide existent phenomenon,it has a complicatied behaviour which is from a deterministic nonlinear dynamical system.Phase space reconstruction is the base of using dynamical methods to analysis nonlinear time series.The key of phase space reconstruction is the estimation of its parameters.Firstly we discuss the theory of phase space reconstruction,then we discuss the methods of choosing embedding dimension and delay time.In this paper we mainly study local prediction,which is based on the maximum broad entropy,we construct a broad distribution describing the chaos attractor to predict chaotic time series.Firstly this paper introduce the basic concepts of chaos and symbolic dynamics,for compact system,which is restricted with the measurement center,it verify that{P_i}*—chaos is usually not equivalent to SS chaos.Secondly we reseach the prediction theory of chaotic time series,by combining fractal geometry theory and the maximum entropy principle,a new mathod of pridicting chaotic time serise is proposed based on phase space reconstruction.Finaly,we provide a conclution aboat this paper and point some unsolved problems.