A wavelet-based tool for studying non-periodicity

TL;DR

This paper introduces a wavelet-based numerical method to quantify non-periodicity in signals, complementing existing chaos detection tools, and demonstrates its effectiveness on classical dynamical systems.

Contribution

A novel scale index parameter derived from wavelet analysis is proposed to measure signal non-periodicity, enhancing chaos transition studies.

Findings

The scale index effectively distinguishes between periodic and non-periodic signals.

Application to classical systems validates the method's accuracy.

The approach complements Lyapunov exponent analysis for chaos detection.

Abstract

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.