Characterization of chaotic attractors at bifurcations in Murali–Lakshmanan–Chua's circuit and one-way coupled map lattice system

Abstract

In the present paper we study certain characteristic features associated with bifurcations of chaos in a finite dimensional dynamical system – Murali–Lakshmanan–Chua (MLC) circuit equation and an infinite dimensional dynamical system – one-way coupled map lattice (OCML) system. We characterize chaotic attractors at various bifurcations in terms of σ n ( q) – the variance of fluctuations of coarse-grained local expansion rates of nearby orbits. For all chaotic attractors the σ n ( q) versus q plot exhibits a peak at q= q α . Additional peaks, however, are found only just before and just after the bifurcations of chaos. We show power-law variation of maximal Lyapunov exponent near intermittency and sudden widening bifurcations. Linear variation is observed for band-merging bifurcation. We characterize weak and strong chaos using probability distribution of k-step difference of a state variable.