Nonlocality of ReactionDiffusion Equations Induced by Delay: Biological Modeling and Nonlinear Dynamics
 S. A. Gourley,
 J. W.H. So,
 J. H. Wu
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We present a short survey on the biological modeling, dynamics analysis, and numerical simulation of nonlocal spatial effects, induced by time delays, in diffusion models for a single species confined to either a finite or an infinite 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 discuss and compare two existing approaches to correctly derive the spatial averaging kernels, and we summarize some of the recent developments in both qualitative and numerical analysis of the nonlinear dynamics, including the existence, uniqueness (up to a translation), and stability of traveling wave fronts and periodic spatiotemporal patterns of the model equations in unbounded domains and the linear stability, boundedness, global convergence of solutions and bifurcations of the model equations in finite domains.
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 Title
 Nonlocality of ReactionDiffusion Equations Induced by Delay: Biological Modeling and Nonlinear Dynamics
 Journal

Journal of Mathematical Sciences
Volume 124, Issue 4 , pp 51195153
 Cover Date
 20041201
 DOI
 10.1023/B:JOTH.0000047249.39572.6d
 Print ISSN
 10723374
 Online ISSN
 15738795
 Publisher
 Kluwer Academic PublishersPlenum Publishers
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 S. A. Gourley ^{(1)}
 J. W.H. So ^{(2)}
 J. H. Wu ^{(3)}
 Author Affiliations

 1. Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey, GU2 7XH, England
 2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada
 3. Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada