MODELING CHAOTIC DYNAMICS WITH DISCRETE NONLINEAR RATIONAL MODELS

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Abstract
This paper investigates the application of discrete nonlinear rational models, a natural extension of the well-known polynomial models. Rational models are discussed in the context of two different problems: reconstruction of chaotic attractors from a time series and the estimation of static nonlinearities from dynamical data. Rational models are obtained via black box identification techniques which only need a relatively short data set. A simple modified algorithm is proposed to handle the noise thus providing a solution to one of the greatest obstacles for estimating rational models from real data. The suggested algorithm and related ideas are tested and discussed using Rössler's equations, real data collected from an implementation of Chua's circuit, logistic map, sine-map with cubic-type nonlinearities, tent map and a map of a feedback buck switching regulator model.