Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 60, Issue 3, Pages 634-641Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2010.05.010
Keywords
Non-periodicity; Wavelets; Chaotic dynamical systems
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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. (C) 2010 Elsevier Ltd. All rights reserved.
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