Recognizing chaotic time-waveforms in terms of a parametrized family of nonlinear predictors

Abstract Consider a chaotic dynamical system which exhibits a variety of chaotic time-waveforms with a change in the bifurcation parameters. This paper presents an algorithm for estimating the underlying bifurcation parameters of the chaotic time-waveforms in experimental situation in which no a priori analytical knowledge of the dynamical system is available. First, we construct “qualitatively similar” parametrized family of nonlinear predictors only from several sets of chaotic time-waveforms. “Qualitatively similar” parametrized family means that the family of nonlinear predictors exhibits “qualitatively similar” bifurcation phenomena as the original. Chaotic time-waveforms are then characterized in terms of the “qualitatively similar” bifurcation parameters of the nonlinear predictors. We call the characterization of chaotic time-waveforms in terms of the underlying bifurcation parameters “chaotic time-waveform recognition”. Several numerical experiments using the Rossler equations show the efficiency of the algorithm. The effect of observational noise included in chaotic time-waveforms is also considered.

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