相空间重构中最优滞时的确定

Determination of Optimal Delay Time in Reconstructing Phase Space

针对混沌理论的相空间重构技术中 ,自相关函数法和互信息函数法在确定延迟时间时存在的不足 ,提出了根据不同嵌套维下的混沌吸引子所包含的信息量Shannon熵随延迟时间 τ的变化情况 ,来确定不同嵌套维下重构混沌吸引子的最优滞时 ,这种方法把物理问题转化为纯几何问题。

In reconstruction of phase space technology , the delay time is usually determined by mutual information or auto relation analysis. However, the delay time determined by mutual information is two dimensional in terms of physics,while the delay time by auto relation analysis characterizes the minimum linear relationship, which is not fitted for chaotic time series.According to the fact that the information of chaotic attractor is variable at different reconstruction condition,a new way is proposed to determine the delay time at different embedding dimension through investigating the Shannon entropy of different chaotic attractor. It transfers a physical problem to a geometric problem and gets rid of the shortcomings of mutual information or auto relation analysis.