Heterogeneous noise-induced extreme events and synchronization in a globally coupled network of FitzHugh-Nagumo oscillators

Abstract

This study investigates the dynamics of a globally coupled network of heterogeneous FitzHugh Nagumo (FHN) oscillators under stochastic influences, with particular emphasis on the emergence of extreme events (EE). While previous studies explored FHN networks subjected to homogeneous noise, revealing behaviors such as noise-induced synchronization, stochastic resonance, and coherence resonance, the impact of noise heterogeneity remains poorly understood. Moreover, the emergence of EE under heterogeneous stochastic excitation has largely been overlooked. To address these gaps, we capture the natural variability in neuronal responses to external stimuli by introducing nonidentical noise sources, thereby reflecting diversity across the network. Our results reveal that EE can arise both globally, where large excursions occur collectively across the entire network, and partially, where only a subset of oscillators exhibits extreme activity depending on the interplay between noise intensity and coupling strength. We further identify three distinct classes of EE that enrich the system's dynamical repertoire and propose a quantitative metric capable of distinguishing between global and local occurrences. Remarkably, we demonstrate that even under heterogeneous noise inputs, noise can synchronize EE across the network, underscoring the robustness of collective dynamics in stochastic regimes. Furthermore, causal interaction analysis between oscillator pairs provides mechanistic insights into the initiation and propagation of EE. To the best of our knowledge, this constitutes the first demonstration of both partially and globally synchronized EE triggered solely by noise in a network of coupled oscillators. These findings enhance our understanding of noise-driven collective behavior in complex systems and provide new insights into neuronal dynamics under random influences.