Abstract
In this paper, we report the occurrence of two distinct types of bursting oscillations (BOs) in a parametrically excited Liénard system. When the system is linearly damped, it undergoes saddle–node bifurcations leading to asymmetric bursting oscillations as the control parameter is varied. On the other hand, if it is damped with a nonlinear force, then it exhibits supercritical pitchfork and supercritical pitchfork/fold bifurcations resulting in symmetric bursting oscillations. We have identified the equilibrium points of the system for both the linear and nonlinear damping cases and have analyzed their stability. We have constructed the bifurcation and two-parameter stability plots to characterize the two distinct bursting oscillations and their transitions. Also, we have proposed an analog electronic model of our system and made real time experimental observations to validate our numerical results.
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