Comparative analysis of pattern formation and resilience in Brusselator networks with linear and nonlinear coupling

The Brusselator, a prototypical model of autocatalytic chemical reactions, serves as a paradigm for studying nonlinear oscillations and pattern formation in reaction-diffusion systems. Here, we investigate the collective dynamics and resilience of a network of coupled Brusselator oscillators under linear and nonlinear coupling schemes. By varying coupling strength and phase-lag parameters, we map the emergent states using the global order parameter and strength of incoherence, identifying synchronized, chimera, traveling-wave, oscillation death, and chimera death regimes. These rich dynamics arise in linearly coupled networks, while nonlinear coupling yields only synchronization, desynchronization, and chimera states, along with a coupling-dependent increase in oscillation frequency, unlike the frequency-invariant linear case. To probe resilience, we apply localized additive perturbations and quantify recovery via recovery time, fraction of affected oscillators, and minimum order parameter. Weak coupling and chimera states exhibit prolonged desynchronization and incomplete recovery, whereas strong coupling enables rapid restoration of coherence. Nonlinear interactions further introduce phase-sensitive responses, leading to oscillatory variations in recovery metrics with coupling strength. Our results represent that coupling nonlinearity critically shapes both the formation and robustness of spatiotemporal patterns. The proposed perturbation framework offers a general, quantitative tool to assess stability in oscillatory networks, with direct relevance to chemical, biological, and engineered systems where resilience to local disturbances is vital.