Dynamics of a food-limited population model incorporating nonlocal delays on a finite domain |
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Authors: | SA Gourley J W-H So |
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Institution: | (1) Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey GU2 7XH, England. e-mail: s.gourley@surrey.ac.uk, UK;(2) Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada, CA |
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Abstract: | 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.
Received: 29 August 2000 / Revised version: 6 March 2001 / Published online: 7 December 2001 |
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