A wavelet-based tool for studying non-periodicity

被引：85

作者：

Benitez, R. ^{[1
]}

Bolos, V. J. ^{[2
]}

Ramirez, M. E.

机构：

[1] Univ Extremadura, Dpto Matemat, Plasencia 10600, Caceres, Spain

[2] Univ Valencia, Dpto Matemat Econ & Empresa, E-46003 Valencia, Spain

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2010年 / 60卷 / 03期

关键词：

Non-periodicity; Wavelets; Chaotic dynamical systems; DUFFING OSCILLATOR; BONHOEFFER-VAN; TIME-SERIES; BIFURCATIONS;

D O I：

10.1016/j.camwa.2010.05.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：634 / 641

页数：8

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