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Spatiotemporal dynamics of a diffusive predator-prey model with nonlocal effect and delay. (English) Zbl 1450.35051
Summary: In this paper, we discuss a diffusive predator-prey model with nonlocality and delay. Stability and bifurcation analysis suggest that the joint impacts of the nonlocal term and delay result in instability of the positive constant steady state. Moreover, steady state, Hopf and steady state-Hopf bifurcations and interactions of these bifurcations may occur under certain conditions. Normal forms of steady state, Hopf and steady state-Hopf bifurcations for a general reaction-diffusion model with nonlocal effects and delay are derived. In numerical simulations, spatially inhomogeneous steady states and periodic solutions and heteroclinic connections between these solutions are obtained.

##### MSC:
 35B32 Bifurcations in context of PDEs 35K57 Reaction-diffusion equations 35K51 Initial-boundary value problems for second-order parabolic systems 35R10 Functional partial differential equations 37L10 Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems 92D25 Population dynamics (general)
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