A wavelet-based tool for studying non-periodicity

Authors:
R. Benítez;V. J. Bolós;M. E. Ramírez
Affiliations:
Dpto. Matemáticas, Univ. Extremadura, 10600 Plasencia, Caceres, Spain;Dpto. Matemáticas para la Economía y la Empresa, Univ. Valencia, Spain;GMV A& D, Spain
Venue:
Computers & Mathematics with Applications
Year:
2010

Citing 1
Cited 1

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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 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.