Suppression of extreme events and chaos in a velocity-dependent potential system with time-delay feedback

TL;DR

This study examines how time-delayed feedback can suppress or induce extreme events and chaos in a velocity-dependent potential system, revealing that positive feedback broadly suppresses extreme events while higher feedback can eliminate chaos.

Contribution

It demonstrates the dual role of time-delayed feedback in controlling extreme events and chaos in a non-polynomial velocity-dependent potential system, with detailed analysis of feedback effects.

Findings

Positive feedback suppresses extreme events over larger parameter regions.

Negative feedback restricts the suppression of extreme events.

Higher feedback values lead to complete chaos suppression.

Abstract

The foremost aim of this study is to investigate the influence of time-delayed feedback on extreme events in a non-polynomial system with velocity dependent potential. To begin, we investigate the effect of this feedback on extreme events for four different values of the external forcing parameter. Among these four values, in the absence of time-delayed feedback, for two values, the system does not exhibit extreme events and for the other two values, the system exhibits extreme events. On the introduction of time-delayed feedback and varying the feedback strength, we found that extreme events get suppressed as well as get induced. When the feedback is positive, suppression occurs for a larger parameter region whereas in the case of negative feedback it is restricted to the limited parameter region. We confirm our results through Lyapunov exponents, probability density function of peaks, $d_{max}$ plot and two parameter probability plot. Finally, we analyze the changes in the overall dynamics of this system under the influence of time-delayed feedback. We notice that complete suppression of chaos occurs in the considered system for higher values of the time-delayed feedback.