Abstract: By using the Hopf bifurcation theory, we studied an arbitrary order autocatalysis reaction-diffusion model with saturation effect. Firstly, the stability of the positive equilibrium points for the ordinary differential system was given, and the existence and stability of Hopf bifurcation were given by taking a as the bifurcation parameter. Secondly, the Turing instability caused by  diffusion was established for diffusion system, and the existence of Hopf bifurcation was given. Finally, some numerical simulation examples were used to verify the correctness of the theoretical analysis results.

Key words: saturation effect, autocatalysis, Turing instability, Hopf bifurcation