Dynamical origin of extreme events in mutually coupled and networked Brusselator

This study investigates the dynamical origins and statistical properties of extreme events (EEs) in a diffusively coupled theoretical Brusselator system, extending from pairwise interactions to globally coupled networks. Statistically, the emergence of EEs is characterized by heavy-tailed probability density functions and exponential interevent interval distributions, alongside an analysis of the complementary cumulative distribution function and return periods. To elucidate the underlying generative mechanism, we employ invariant manifold computations and vector field divergence analysis. Our results demonstrate that EEs are triggered by a critical region formed by the geometric alignment of stable and unstable manifolds near a saddle-type invariant set governed by the Shilnikov mechanism. Furthermore, extending the analysis to a globally coupled network reveals that network dimensionality does not affect the prevalence of EEs. Finally, these numerical findings are corroborated by experimental observations from an analog electronic circuit, confirming the robustness of these dynamical phenomena in physical systems.