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A predator-prey reaction-diffusion system with nonlocal effects. (English) Zbl 0840.92018

Summary: We consider a predator-prey system in the form of a coupled system of reaction-diffusion equations with an integral term representing a weighted average of the values of the prey density function, both in past time and space. In a limiting case the system reduces to the Lotka Volterra diffusion system with logistic growth of the prey. We investigate the linear stability of the coexistence steady state and bifurcations occurring from it, and expressions for some of the bifurcating solutions are constructed. None of these bifurcations can occur in the degenerate case when the nonlocal term is in fact local.

MSC:

92D25 Population dynamics (general)
35K57 Reaction-diffusion equations
35B35 Stability in context of PDEs
35B32 Bifurcations in context of PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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