Different transitions of bursting and mixed-mode oscillations in Liénard system

Abstract

In this paper, we present the emergence of bursting oscillations, mixed-mode oscillations and transient chaos in the forced Liénard system. The system exhibits intriguing dynamical transitions such as from chaotic bursting oscillations to spiking trains via periodic bursting oscillations, period doubling mixed-mode oscillations route to chaos, and intermittent mixed-mode oscillations on variation of the nonlinear damping coefficient as the control parameter. In addition, the system transits from spiking trains to chaotic bursting oscillations through successive period adding sequences of bursting oscillations upon variation of the strength of nonlinearity. Besides the system exhibits transient chaos also. We believe that it is for the first time that these multiplicity of dynamical behaviors and transitions are reported in a single model. We validate our numerical investigations with the help of experimental observations using a simple nonlinear electronic circuit implementation of the model.