A wavelet-based tool for studying non-periodicity

Details A wavelet-based tool for studying non-periodicity A wavelet-based tool for studying non-periodicity

2010-07-20

arxiv.org/abs/1007.3373v1

Comput. Math. Appl. 60 (2010), 634-641

Nonlinear Sciences

Chaotic Dynamics

14 pages, 6 figures

Scientific paper

10.1016/j.camwa.2010.05.010

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.

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