Parametric excitation induced extreme events in MEMS and Lienard oscillator

TL;DR

This paper investigates how parametric excitation can induce extreme events in nonlinear oscillators, including MEMS and Lienard systems, revealing bifurcation routes and energy mechanisms behind these rare, large amplitude occurrences.

Contribution

It provides the first theoretical analysis of extreme events in parametrically excited MEMS and Lienard oscillators, identifying bifurcation routes and energy dynamics responsible for EEs.

Findings

EEs emerge via bifurcation routes: intermittency and period-doubling.

Inter-event intervals follow Poisson-like distribution, indicating rarity.

EEs are linked to stick-slip bifurcation near system boundaries.

Abstract

The two paradigmatic nonlinear oscillatory models with parametric excitation are studied. The authors provide theoretical evidence for the appearance of extreme events (EEs) in those systems. First, the authors consider a well known Lienard type oscillator that shows the emergence of EEs via two bifurcation routes: Intermittency and period-doubling routes for two different critical values of the excitation frequency. The authors also calculate the return time of two successive EEs, defined as inter-event intervals, that follow Poisson-like distribution, confirm the rarity of the events. Further, the total energy of the Lienard oscillator is estimated to explain the mechanism for the development of EEs. Next, the authors confirmed the emergence of EEs in a parametrically excited microelectromechanical system. In this model, EEs occur due to the appearance of stick-slip bifurcation near the discontinuous boundary of the system. Since the parametric excitation is encountered in several real-world engineering models, like macro and micromechanical oscillators, the implications of the results presented in this paper are perhaps beneficial to understand the development of EEs in such oscillatory systems.