Emergence and mitigation of extreme events in a parametrically driven system with velocity-dependent potential

TL;DR

This paper investigates the emergence of extreme events in a parametrically driven nonlinear mechanical system with velocity-dependent potential, and demonstrates how external driving can mitigate these events, with noise effects leading to super-extreme events.

Contribution

It introduces a novel analysis of extreme events in a non-polynomial system and shows how external drive can suppress these events, including effects of noise on their persistence and transformation.

Findings

Extreme events follow a long-tail distribution in the system.

External drive can effectively suppress extreme events.

Noise influences the persistence and transformation of extreme events.

Abstract

In this paper, we discuss the emergence of extreme events in a parametrically driven non-polynomial mechanical system with a velocity-dependent potential. We confirm the occurrence of extreme events from the probability distribution function of the peaks, which exhibits a long-tail. We also present the mechanism for the occurrence of extreme events. We found that the probability of occurrence of extreme events alternatively increase and decrease with a brief region where the probability is zero. At the point of highest probability of extreme events, when the system is driven externally, we find that the probability decreases to zero. Our investigation confirms that the external drive can be used as an useful tool to mitigate extreme events in this nonlinear dynamical system. Through two parameter diagrams, we also demonstrate the regions where extreme events gets suppressed. In addition to the above, we show that extreme events persits when the sytem is influenced by noise and even gets transformed to super-extreme events when the state variable is influenced by noise.