Extreme events in MLC circuit

TL;DR

This paper investigates the emergence of extreme events in the Murali-Lakshmanan-Chua (MLC) circuit, revealing how chaotic attractor expansion, external forcing, and phase space dynamics contribute to large deviations.

Contribution

It provides a detailed dynamical analysis of extreme events in the MLC circuit, highlighting the roles of attractor expansion, external force, and phase space decomposition.

Findings

Chaotic attractor expansion via PM intermittency precedes extreme events.

External periodic force induces large deviations leading to extreme events.

Extreme value theory confirms the statistical nature of extreme events.

Abstract

The Murali-Lakshmanan-Chua (MLC) circuit is a well-recognized prominent nonlinear, nonautonomous, and dissipative electronic circuit having a versatile chaotic nature. Unraveling the dynamical synergy responsible for the genesis of extreme events in nonlinear dynamical systems is a prolific and spellbinding research area. The present study unveils the dynamical exposition of emerging extreme events in the MLC circuit concerning two different events being defined in the system. The large expansion of the chaotic attractor following the PM intermittency route plays the crucial role as the precursor behind the emergence of extreme events in the system. Our main finding reveals the prevalence of a force field due to the presence of externally applied periodic force in the system that creates the dynamical synergy that compels the chaotic trajectory traversing in its phase space to be largely deviated from the residing space, and this large deviation shows the signature of extreme events. Apart from the force field explication, we explored another two dynamical aspects that also interpret the mechanism behind the genesis of extreme events as the large deflection of the chaotic trajectory in the system: the decomposition of the phase space in stable and unstable manifolds concerning slow-fast dynamics and using Floquet multipliers. These two different aspects of calculations of the stable and unstable manifolds explicate the large excursion of the chaotic trajectory as extreme events from two different perspectives. We also analyzed the rare occurrences of the extreme events statistically using extreme value theory: the threshold \textit{excess values} follow the generalized Pareto distribution, and the inter-extreme-spike-intervals follow the generalized extreme value distribution.