Analysis of a Brusselator reaction-diffusion model with nonlinear inhibition

In this paper, the pattern formation of a Brusselator reaction-diffusion model with nonlinear inhibition was investigated. Through linear stability analysis and spectral theory, mathematical criteria for the existence and stability of spatial patterns were established. The main results included explicit stability conditions for homogeneous steady states and spectral criteria linking eigenvalue multiplicities to pattern existence. A series of numerical simulations were performed to validate theoretical predictions, revealing clear transitions between uniform and spatially heterogeneous solutions. The work provides fundamental insights into pattern-forming mechanisms for controlling spatial organization in nonlinear reaction-diffusion systems.