Detecting switch dynamics in chaotic time-waveform using a parametrized family of nonlinear predictors

An algorithm is presented for detecting switch dynamics in chaotic time-waveform. By the “switch dynamics,” we mean that the chaotic time-waveform is measured from a dynamical system whose bifurcation parameters are occasionally switched among a set of slightly different parameter values. First, the switched chaotic time-waveform is divided into windows of short-term time-waveforms. From the set of windowed time-waveforms, “qualitatively similar” parametrized family of nonlinear predictors is constructed. “Qualitatively similar” parametrized family means that the family of nonlinear predictors exhibits “qualitatively similar” bifurcation phenomena as the original. By characterizing the windows of short-term chaotic time-waveforms in terms of the “qualitative” parameters of nonlinear predictors, switch dynamics of their associated bifurcation parameters are detected. For the Lorenz equations, the Rössler equations, and the Mackey–Glass equations, efficiency of the algorithm is demonstrated. In the experiment, chaotic time-waveforms contaminated with observational noise is considered.