On the dynamics of the diffusive Field-Noyes model for the Belousov-Zhabotinskii reaction

In this paper, a diffusive Field-Noyes model for the Belousov-Zhabotinskii reaction is considered. We are mainly concerned with the global existence, boundedness and the asymptotic behaviors of the solutions. Of our particular interests, we focus on the existence of attraction region which attracts all the solutions of the system (regardless of the initial values), the global asymptotic stability of the constant positive equilibrium solution, the lumped parameter phenomenon, as well as Turing instability of the spatially homogeneous periodic solutions. In particular, a general formula in terms of the diffusion rates for the general 3×3 reaction-diffusion system is derived to determine Turing instability of the Hopf bifurcating periodic solutions, which extends our earlier results on general 2×2 reaction-diffusion system.