Noise-Induced Localized Patterns in Excitable Media: Amplitude versus Persistence

Abstract

Transient spatially localized activity underlies a broad range of biological processes, yet the statistical property of fluctuations that controls its nucleation remains unclear. We systematically investigate noise-induced dynamics in a spatially extended FitzHugh-Nagumo excitable system and identify three regimes: a quiescent phase, a spatially extended alternating phase, and a pattern-forming phase characterized by transient localized excitation patches. Surprisingly, we find that temporal noise correlations are not required for patch formation: Gaussian white noise produces localized patches when its amplitude is sufficiently large, whereas weaker fluctuations can achieve the same effect when temporal correlations allow them to persist. Our results identify the instantaneous amplitude and the persistence as joint stochastic control parameters for transient pattern formation in excitable media. These distinct quantities are linked through the integrated noise strength, which quantifies the accumulated stochastic forcing available to nucleate an excitation. In addition, the inhibitor response time subsequently determines whether the excitation remains localized or spreads throughout the system.