Constant Bias and Weak Second Periodic Forcing : Tools to Mitigate Extreme Events

TL;DR

This paper introduces two non-feedback methods, constant bias and weak second periodic forcing, to effectively suppress extreme events in nonlinear dynamical systems, demonstrated on Liénard and non-polynomial mechanical systems.

Contribution

The paper presents novel non-feedback techniques for mitigating extreme events in nonlinear systems, including phase adjustment in forcing to enhance suppression.

Findings

Constant bias reduces large amplitude oscillations in Liénard system.

Weak second periodic forcing suppresses extreme events by increasing oscillation amplitudes.

Phase adjustment in forcing further decreases the probability of extreme events.

Abstract

We propose two potentially viable non-feedback methods, namely (i) constant bias and (ii) weak second periodic forcing as tools to mitigate extreme events. We demonstrate the effectiveness of these two tools in suppressing extreme events in two well-known nonlinear dynamical systems, namely (i) Li\'enard system and (ii) a non-polynomial mechanical system with velocity dependent potential. As far as the constant bias is concerned, in the Li\'enard system, the suppression occurs due to the decrease in large amplitude oscillations and in the non-polynomial mechanical system the suppression occurs due to the destruction of chaos into a periodic orbit. As far as the second periodic forcing is concerned, in both the examples, extreme events get suppressed due to the increase in large amplitude oscillations. We also demonstrate that by introducing a phase in the second periodic forcing one can decrease the probability of occurrence of extreme events even further in the non-polynomial system. To provide a support to the complete suppression of extreme events, we present the two parameter probability plot for all the cases. In addition to the above, we examine the feasibility of the aforementioned tools in a parametrically driven version of the non-polynomial mechanical system. Finally, we investigate how these two methods influence the multistability nature in the Li\'enard system.