CLASSIFICATION OF BIFURCATIONS AND ROUTES TO CHAOS IN A VARIANT OF MURALI–LAKSHMANAN–CHUA CIRCUIT

Abstract

We present a detailed investigation of the rich variety of bifurcations and chaos associated with a very simple nonlinear parallel nonautonomous LCR circuit with Chua's diode as its only nonlinear element as briefly reported recently [Thamilmaran et al., 2000]. It is proposed as a variant of the simplest nonlinear nonautonomous circuit introduced by Murali, Lakshmanan and Chua (MLC) [Murali et al., 1994]. In our study we have constructed two-parameter phase diagrams in the forcing amplitude-frequency plane, both numerically and experimentally. We point out that under the influence of a periodic excitation a rich variety of bifurcation phenomena, including the familiar period-doubling sequence, intermittent and quasiperiodic routes to chaos as well as period-adding sequences, occur. In addition, we have also observed that the periods of many windows satisfy the familiar Farey sequence. Further, reverse bifurcations, antimonotonicity, remerging chaotic band attractors, and so on, also occur in this system. Numerical simulation results using Poincaré section, Lyapunov exponents, bifurcation diagrams and phase trajectories are found to be in agreement with experimental observations. The chaotic dynamics of this circuit is observed experimentally and confirmed both by numerical and analytical studies as well PSPICE simulation results. The results are also compared with the dynamics of the original MLC circuit with reference to the two-parameter space to show the richness of the present circuit.