Route to extreme events in excitable systems

TL;DR

This paper investigates how interior crises in FitzHugh-Nagumo systems with various coupling topologies lead to rare, recurrent extreme events, highlighting the role of mixed-mode oscillations and chaotic dynamics.

Contribution

It identifies interior crises as key organizers of extreme events in excitable systems and demonstrates their robustness across different system sizes.

Findings

Extreme events are linked to interior crises in the system.

The phenomenon persists across different coupling topologies.

Extreme events occur in specific parameter regions and are robust to system size.

Abstract

Systems of FitzHugh-Nagumo units with different coupling topologies are capable of self-generating and -terminating strong deviations from their regular dynamics that can be regarded as extreme events due to their rareness and recurrent occurrence. Here we demonstrate the crucial role of an interior crisis in the emergence of extreme events. In parameter space we identify this interior crisis as the organizing center of the dynamics by employing concepts of mixed-mode oscillations and of leaking chaotic systems. We find that extreme events occur in certain regions in parameter space, and we show the robustness of this phenomenon with respect to the system size.