Hopf bifurcation and Turing instability of 2-D Lengyel–Epstein system with reaction–diffusion terms

In this paper, we study 2-D Lengyel–Epstein (L–E) reaction–diffusion system with homogeneous Neumann boundary condition. By employing stability theory, Hopf bifurcation theorem and Turing’s theory, we present some sufficient conditions ensuring the equilibrium point of system to be stable and derive conditions on the parameters so that spatial homogenous Hopf bifurcation and Turing instability occur. These conditions obtained have important leading significance in applications of L–E system. Finally, we show some numerical examples to verity the theoretical analysis.