Chaos in Jerky flow: theory and experiment

Abstract

Recently, the prediction of chaos in jerky flow based on a nonlinear dynamical model has been verified by demonstrating the existence of correlation dimension for the stress signals obtained on samples of AlCu alloys. However, an unambiguous support of chaos requires the existence of a positive Lyapunov exponent. Here we consider a recent method which uses state space reconstruction by embedding the signals in higher dimension and obtaining the signature of chaos using the property of divergence of near by orbits. The method provides a reasonable estimate of the delay time and the embedding dimension. We first illustrate the method by using the time series obtained from a dynamical model and then apply it to the experimental signals. The analysis shows that the experimental signals are truly chaotic. The minimum number of variables required for the dynamical description of jerky flow appears to be five, consistent with the estimate of the correlation dimension.