Extreme events in the Lienard system with asymmetric potential: An in-depth exploration

TL;DR

This paper explores how asymmetric potentials in a forced Lienard oscillator lead to rare extreme events, analyzing their emergence, control, and underlying dynamics through bifurcation, Lyapunov exponents, and phase diagrams.

Contribution

It reveals the impact of asymmetry on extreme events in the Lienard system and demonstrates control methods using damping, advancing understanding of nonlinear dynamical behaviors.

Findings

Asymmetry reduces the frequency of well-jumping and induces rare extreme events.

Bifurcation diagrams and Lyapunov exponents characterize the system's chaotic behavior.

Damping can effectively control the occurrence of extreme events.

Abstract

This research investigates the dynamics of a forced Lienard oscillator featuring asymmetric potential wells. We provide compelling evidence of extreme events (EE) in the system by manipulating the height of the potential well. In the case of a symmetric well, the system exhibits chaotic behavior, with the trajectory irregularly traversing between the two wells, resulting in frequent large oscillations under specific parameter values. However, the introduction of asymmetry in the potential wells induces a noteworthy transformation. The frequency of jumping between wells is significantly diminished. In essence, the system trajectory displays rare yet recurrent hops to the adjacent well, which we identify as EE. The intricate dynamical behavior observed in the system is elucidated through bifurcation diagrams and Lyapunov exponents. The emergence of EE in the system, governed by various parameters, is characterized using the threshold height, probability distribution function, and inter-event intervals. We illustrate the regions of EE using phase diagram plots and demonstrate the control of EE by incorporating a damping term into the system.