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RESEARCH PRODUCT

A wavelet-based tool for studying non-periodicity

M. E. RamírezRafael BenítezVicente J. Bolós

subject

Dynamical systems theoryFOS: Physical sciencesLyapunov exponentDynamical Systems (math.DS)37D99 42C40WaveletsDynamical systemMeasure (mathematics)symbols.namesakeWaveletModelling and SimulationFOS: MathematicsApplied mathematicsMathematics - Dynamical SystemsContinuous wavelet transformMathematicsMathematical analysisNonlinear Sciences - Chaotic DynamicsNon-periodicityHénon mapNonlinear Sciences::Chaotic DynamicsComputational MathematicsComputational Theory and MathematicsModeling and SimulationsymbolsLogistic mapChaotic Dynamics (nlin.CD)Chaotic dynamical systems

description

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.

yearjournalcountryeditionlanguage
2010-08-01
10.1016/j.camwa.2010.05.010http://arxiv.org/abs/1007.3373