Bursting Oscillations and Mixed-Mode Oscillations in Driven Liénard System

Abstract

We report the existence of bursting oscillations and mixed-mode oscillations in a Liénard system when it is driven externally by a sinusoidal force. The bursting oscillations transit from a periodic phase to spiking trains through chaotic windows, as the control parameter is varied. The mixed-mode oscillations appear via an alternate sequence of periodic and chaotic states, as well as Farey sequences. The primary and their associated secondary mixed-mode oscillations are detected for the suitable choices of system parameters. Additionally, the system is also found to possess multistability nature. Our investigations involve numerical simulations as well as real time hardware experiments using a simple analog electronic circuit. The experimental observations are in conformation with numerical results.