4.4 Article

BIFURCATION ANALYSIS OF A GENERAL ACTIVATOR-INHIBITOR MODEL WITH NONLOCAL DISPERSAL

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Summary: The study explores the stability of a constant steady state in a general reaction-diffusion model with nonlocal dispersal of activator or inhibitor, and finds that Turing instability and spatial patterns can be induced by fast nonlocal inhibitor dispersal and slow activator diffusion. It also shows that slow nonlocal activator dispersal causes instability without producing stable spatial patterns. The existence of nonconstant positive steady states is demonstrated through bifurcation theory, suggesting a new mechanism for spatial pattern formation different from the traditional Turing mechanism. The theoretical results are applied to pattern formation problems in nonlocal water-plant and predator-prey models.

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