Temporal Dynamics beyond the Exceptional Point in the Ikeda Map with Balanced Gain and Loss

TL;DR

This paper explores the complex temporal behaviors of the Ikeda Map with balanced gain and loss, revealing period doubling, chaos, and extreme events beyond the exceptional point through bifurcation and Lyapunov analysis.

Contribution

It demonstrates the emergence of chaotic dynamics and extreme events in the Ikeda Map with balanced gain and loss beyond the exceptional point, extending understanding of nonlinear optical systems.

Findings

Period quadrupling at the exceptional point

Chaotic dynamics beyond the EP

Onset of Extreme Events via attractor merging crisis

Abstract

We investigate the temporal dynamics of the Ikeda Map with Balanced Gain and Loss and in the presence of feedback loops with saturation nonlinearity. From the bifurcation analysis, we find that the temporal evolution of optical power undergoes period quadrupling at the exceptional point (EP) of the system and beyond that, chaotic dynamics emerge in the system and this has been further corroborated from the Largest Lyapunov Exponent (LLE) of the model. For a closer inspection, we analyzed the parameter basin of the system, which further leads to our inference that the Ikeda Map with Balanced Gain and Loss exhibits the emergence of chaotic dynamics beyond the exceptional point (EP). Furthermore, we find that the temporal dynamics beyond the EP regime leads to the onset of Extreme Events (EE) in this system via attractor merging crisis.