Journal
JOURNAL OF MATHEMATICAL BIOLOGY
Volume 44, Issue 1, Pages 49-78Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s002850100109
Keywords
time-delay; nonlocal; reaction-diffusion; food-limited model
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In this paper 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.
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