Extreme forcing and wave dynamics in weakly nonlocally coupled excitable FitzHugh-Nagumo systems

TL;DR

This paper investigates how extreme external forcing, including noise and pulses, affects wave dynamics in coupled FitzHugh-Nagumo systems, revealing diverse synchronization and propagation regimes.

Contribution

It provides a comprehensive classification of dynamical regimes induced by various types of extreme external forcing in weakly nonlocal FitzHugh-Nagumo systems.

Findings

Periodic forcing induces synchronization tongues and multiple traveling waves.

Lévy noise suppresses regular behavior and causes counter-propagating waves.

Increasing noise intensity leads to transition from organized waves to random walking dynamics.

Abstract

The influence of extreme external forcing on traveling-wave dynamics in an ensemble of weakly nonlocally coupled excitable FitzHugh--Nagumo systems is studied. Three types of external exposure are considered: periodic Gaussian pulses, periodic pulses modulated by Gaussian white noise, and L\'evy noise with tunable distribution parameters. Periodic forcing produces synchronization tongues with highly regular collective dynamics and may induce multiple traveling waves or coexistence of partial synchronization with wave propagation. In contrast, L\'evy noise suppresses regular behavior and generates a regime of counter-propagating waves, which with increasing intensity transitions to random walking dynamics. The study provides a comprehensive classification of the observed dynamical regimes and presents their organization in parameter space for different types of extreme external forcing.