Abstract
This paper is devoted to a general Brusselator model with cross-diffusion under Neumann boundary conditions. We mainly consider the instability effect of cross-diffusion on stable periodic solutions bifurcating from the unique positive equilibrium. According to Floquet theory and implicit function existence theorem, we establish some conditions on the self-diffusion and cross-diffusion coefficients under which the stable Hopf bifurcation periodic solutions can become unstable. The instability of stable spatial homogeneous periodic solutions will lead to the emergence of new irregular spatiotemporal patterns. Finally, we provide numerical simulations to support our analytical findings.
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