Spatial pattern formation in activator-inhibitor models with nonlocal dispersal

The stability of a constant steady state in general reaction-diffusion activator-inhibitor model with nonlocal dispersal the activator or inhibitor is considered. It shown that Turing type instability and associated spatial patterns can be induced by fast slow diffusion, also causes but may not produce stable patterns. The existence nonconstant positive states through bifurcation theory. This suggests new mechanism for pattern formation, which has different parameter regime compared to mechanism. theoretical results are applied formation problems Klausmeier-Gray-Scott water-plant Holling-Tanner predator-prey model.