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Dynamics of a food-limited population model incorporating nonlocal delays on a finite domain. (English) Zbl 0993.92027

We model and analyse nonlocal spatial effects, induced by time delays, in a diffusion model for a single species confined to a finite domain. The nonlocality, a weighted average in space, arises when account is taken of the fact that individuals have been at different points in space at previous times. We show how to correctly derive the spatial averaging kernels for finite domain problems, generalising the ideas of other investigators who restricted attention to the simpler case of an infinite domain. The resulting model is then analysed and results established on linear stability, boundedness, global convergence of solutions and bifurcations.

MSC:

92D25 Population dynamics (general)
35K99 Parabolic equations and parabolic systems
35B35 Stability in context of PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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