RECONSTRUCTION OF NONLINEAR TIME-DELAY MODELS FROM DATA BY THE USE OFOPTIMAL TRANSFORMATIONS

We propose a new technique for the numerical reconstruction of non-lin ear delay differential equations from time series by applying the meth od of optimal transformations, a concept of multiple non-linear regres sion analysis. By constructing a generalized correlation function, thi s method allows for testing time series for delay-induced dynamics. Al so, the delay times and the governing differential equations are estim ated with good numerical accuracy. We present several examples which s how that this method is useful also for the analysis of short and nois y time series. (C) 1997 Elsevier Science B.V.