A nonlinear prediction technique for parametrized families of chaotic dynamics

A simple algorithm is proposed for reconstruction of parametrized families of chaotic dynamics. This algorithm enables one to generate bifurcation diagrams which are qualitatively the same as the original ones only from several time-waveforms, without knowing an explicit form of the dynamics and information of the parameter values. The algorithm consists of two steps. First, globally smooth nonlinear predictors are computed for all time waveforms. Second, the Karhunen-Loéve transform is used to find only significant parameters contributing to the bifurcations. The algorithm is tested against two parametrized families of dynamics: the Hénon family and the coupled logistic/delayed-logistic family. © 1997 John Wiley & Sons, Inc.