A Discriminant Procedure for the Solution of Inverse Problems for Nonstationary Systems

Abstract

The inverse problem of nonlinear dynamics is analyzed, with reference to nonstationary chaotic systems. Numerical procedures are developed for the reconstruction of differential equations directly from experimental series. To consider the procedure of model identification in state space, a differential identification scheme along two time intervals (windows) has been introduced, typical of discriminant analysis. Such a scheme is shown to reliably detect nonstationarities caused by changes both in control parameters of the system itself and external forces. High sensitivity of the differential schemes to the parameter variation is also exhibited in the specific case while determining the model type. The efficiency of such a procedure is demonstrated using the examples of a noisy discrete map and the Rossler chaotic system with step-wise and sinusoidally varying changes in control parameter. The differential procedure suggested is capable of revealing abrupt control parameter changes as small as 0.5%, whereas standard procedures of statistical discrimination such as average value and variance show no any meaningful changes in similar conditions.