A wavelet-based tool for studying non-periodicity
Chaotic Dynamics
2016-08-14 v1 Dynamical Systems
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.
Cite
@article{arxiv.1007.3373,
title = {A wavelet-based tool for studying non-periodicity},
author = {R. Benítez and V. J. Bolós and M. E. Ramírez},
journal= {arXiv preprint arXiv:1007.3373},
year = {2016}
}
Comments
14 pages, 6 figures