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

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.