From quenching to revival: The role of intrinsic noise in heterogeneous coupled Brusselators

In this work, we investigate the stochastic dynamics of diffusively coupled Brusselators, focusing on the interplay between intrinsic noise and coupling in small systems composed of two and three oscillators. Stochasticity is incorporated by explicitly modeling the underlying chemical reaction events through the Gillespie algorithm. As the coupling constant increases, the system exhibits a non-monotonic dynamical response in which sustained oscillations are first suppressed and subsequently revived in synchrony. Our results show that this behavior arises exclusively in heterogeneous systems, where the coupled oscillators differ by a minimal amount in their intrinsic noise levels, while all other parameters remain identical. In the two-oscillator system, the suppression of spiking occurs abruptly and is consistent with a mechanism associated with a homoclinic-like bifurcation. In contrast, the three-oscillator system exhibits multiple dynamical pathways toward oscillation quenching, reflecting the interplay between noise heterogeneity and collective interactions. These findings reveal the emergence of distinct dynamical phases governed by the combined effects of coupling strength and intrinsic stochasticity. Overall, our results demonstrate that intrinsic noise can qualitatively reshape the collective dynamics of coupled chemical oscillators. In particular, the suppression and subsequent revival of synchronized spiking reported here originate purely from stochastic effects and, therefore, have no counterpart in the deterministic Brusselator model, highlighting the role of noise as an effective control mechanism for rhythmic activity in nonlinear systems.