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Spatial structures and periodic travelling waves in an integro- differential reaction-diffusion population model. (English) Zbl 0723.92019

An integro-differential reaction-diffusion equation is derived for the dynamics of a population for which local aggregation can be advantageous, while intra-specific competition is modeled nonlocally in space and time by means of a spatial and temporal convolution term. Spatial and temporal patterns are studied using bifurcation and linearized stability techniques.
Three kinds of bifurcations from the uniform steady state are considered: (i) steady spatially periodic structures, (ii) periodic standing wave solutions, and (iii) periodic travelling wave solutions.

MSC:

92D25 Population dynamics (general)
35K57 Reaction-diffusion equations
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92D40 Ecology
35B32 Bifurcations in context of PDEs
45K05 Integro-partial differential equations
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