Synchronization and extreme events in multiplex FitzHugh-Nagumo networks under heterogeneous noise

Neuronal systems are highly susceptible to noise, which can trigger erratic, abrupt, and sudden dynamical transitions known as extreme events (EEs). The FitzHugh-Nagumo (FHN) model, a minimal yet powerful two-dimensional representation of neuronal dynamics, has been extensively employed to investigate noise-induced behaviors in both single neurons and monolayer networks. In this work, we extend these studies to a multiplex network consisting of two layers of FHN oscillators with non-local coupling, where each layer is exposed to heterogeneous noise. Our results demonstrate that at low-noise intensities, the probability of EE occurrence increases when neurons exhibit weak synchronization. This weak synchrony acts as a precursor that facilitates the onset of collective firing. However, as the network approaches complete synchrony, the probability of EE decreases sharply and can be entirely suppressed by strengthening the inter-layer coupling. In contrast, at high-noise intensities, EEs disappear in the weakly synchronized regime but re-emerge in the strongly synchronized regime. This reappearance of synchronized EE highlights the critical interplay between noise and coupling. Notably, the observed emergence of EE at both low- and high-noise levels is robust across all coupling ranges from local to global connectivity. These findings provide deeper insight into the mechanisms governing EE generation and neuronal synchronization, offering potential implications for understanding seizure-like dynamics in biological neural systems.