Transition to hyperchaos and rare large-intensity pulses in Zeeman laser

TL;DR

This paper investigates the sudden transition to hyperchaos in the Zeeman laser model, linking it to large-intensity pulses and extreme events, and explores its robustness and distinct features compared to regular chaos.

Contribution

It identifies a discontinuous transition to hyperchaos associated with large pulses in the Zeeman laser, highlighting the phenomenon's robustness and the need for new metrics to distinguish it from chaos.

Findings

Hyperchaos occurs abruptly at critical parameters in the Zeeman laser model.

Large-intensity pulses are recurrent and exhibit extreme event characteristics.

The transition to hyperchaos shows hysteresis only in specific cases.

Abstract

A discontinuous transition to hyperchaos is observed at discrete critical parameters in the Zeeman laser model for three well known nonlinear sources of instabilities, namely, quasiperiodic breakdown to chaos followed by interior crisis, quasiperiodic intermittency, and Pomeau-Manneville intermittency. Hyperchaos appears with a sudden expansion of the attractor of the system at a critical parameter for each case and it coincides with triggering of occasional and recurrent large-intensity pulses. The transition to hyperchaos from a periodic orbit via Pomeau-Manneville intermittency shows hysteresis at the critical point, while no hysteresis is recorded during the other two processes. The recurrent large-intensity pulses show characteristic features of extremes by their height larger than a threshold and probability of rare occurrence. The phenomenon is robust to weak noise although the critical parameter of transition to hyperchaos shifts with noise strength. This phenomenon appears as common in many low dimensional systems as reported earlier, there the emergent large-intensity events or extreme events dynamics have been recognized simply as chaotic in nature although the temporal dynamics shows occasional large deviations from the original chaotic state in many examples. We need a new metric, in the future, that would be able to classify such significantly different dynamics and distinguish from chaos.