一种基于小波的非周期性研究工具
A wavelet-based tool for studying non-periodicity
摘要：
本文提出了一种新的数值方法来研究信号的非周期性，它可以补充最大李雅普诺夫指数方法来确定一个给定的动力系统的混沌过渡。该方法基于连续小波变换和小波多分辨率分析。引入了一个新参数\textit{scale index}，并将其解释为信号非周期性程度的度量。这种方法被成功地应用到三个经典的动力系统：Bonhoven-van der Pol振荡器，逻辑映射，和Henon映射。
英文摘要：
This paper presents a new numerical approach to the study of non-periodicity in signals, which can complement the maximal Lyapunov exponent method for determining chaos transitions of a given dynamical system. The proposed technique is based on the continuous wavelet transform and the wavelet multiresolution analysis. A new parameter, the \textit{scale index}, is introduced and interpreted as a measure of the degree of the signal's non-periodicity. This methodology is successfully applied to three classical dynamical systems: the Bonhoeffer-van der Pol oscillator, the logistic map, and the Henon map.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
