# Extreme events in Fitzhugh-Nagumo oscillators coupled with two time delays

## TL;DR

This paper investigates complex synchronization and chaotic behaviors in coupled FitzHugh-Nagumo oscillators with one or two time delays, revealing intricate dynamics and bifurcation phenomena.

## Contribution

It introduces analysis of how multiple delays influence synchronization stability and chaotic events in FitzHugh-Nagumo oscillator networks.

## Key findings

- Delay length affects synchronization stability and oscillation modes.
- Two delays induce irregular oscillation patterns and chaotic dynamics.
- Transient chaos occurs between bubbling transition and blowout bifurcation.

## Abstract

We study two identical FitzHugh-Nagumo oscillators which are coupled with one or two different time delays. If only a single delay coupling is used, the length of the delay determines whether the synchronization manifold is transversally stable or unstable, exhibiting mixed mode or chaotic oscillations in which the small amplitude oscillations are always in-phase but the large amplitude oscillations are in-phase or out-of-phase respectively. For two delays we find an intricate dynamics which comprises an irregular alteration of small amplitude oscillations, in-phase and out-of-phase large amplitude oscillations, also called events. This transient chaotic dynamics is sandwiched between a bubbling transition and a blowout bifurcation.