Cross-diffusion induced Turing instability of Hopf bifurcating periodic solutions in the reaction-diffusion enzyme reaction model

Aiming at the spatial pattern phenomenon in biochemical reactions, an enzyme-reaction Sporns-Seelig model with cross-diffusion is chosen as study object. Applying the central manifold theory, normal form method, local Hopf bifurcation theorem and perturbation theory, we study Turing instability of the spatially homogeneous Hopf bifurcation periodic solutions. At last, the theoretical results are verified by numerical simulations.