Diffusion-driven instability and bifurcation in the Lengyel–Epstein system

Lengyel–Epstein reaction–diffusion system of the CIMA reaction is considered. We derive the precise conditions on the parameters so that the spatial homogenous equilibrium solution and the spatial homogenous periodic solution become Turing unstable or diffusively unstable. We also perform a detailed Hopf bifurcation analysis to both the ODE and PDE models, and derive conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution.