【摘要】 介绍基于确定吸收子维数上界检测混沌的 L ID算法 ,与关联数检测混沌算法比较该算法具有两个优点 :可以区分出分形噪声和混沌 ;可以在较低信噪比的情况下进行有效的检测。由于普遍利用基于 SVD分解的 L ID算法在有噪声的情况下阈值很难确定 ,本文分析了 SVD分解计算 L ID缺陷的原因 ,并在此基础上提出了一种基于局部 Neymark分解计算 L ID检测混沌的算法 ,仿真表明取得了很好的结果更多还原

【Abstract】 The application of improved local intrinsic dimension within the context of chaotic time series analysis is presented. After a brief review of this popular method used in nonlinear analysis, we show how the improved version may lead to some significant improvement. First, compared with the GP algorithm, it can distinguish low dimensional chaos from fractal noises, linear stochastic processes and high dimensional chaos. Secondly, since the detection of using the basic local intrinsic dimensional algorithm may lead suspicious result in a short and noisy time series, the widespread usefulness of the method is limited. When applying the algorithm, we use the local Neymark decomposition instead of the local singular value decomposition which is the most important part in the local intrinsic dimension algorithm. Simulated results indicate that the proposed algorithm works better than the basic local intrinsic dimension algorithm in short and noisy chaotic time series.更多还原