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Contemporary Mathematics. Fundamental Directions, 2003, Volume 1, Pages 84–120
(Mi cmfd33)
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This article is cited in 171 scientific papers (total in 171 papers)
Nonlocality of Reaction-Diffusion Equations Induced by Delay: Biological Modeling and Nonlinear Dynamics
S. A. Gourleya, J. W.-H. Sob, Wu Jian Hongc a University of Surrey
b University of Alberta
c York University
Abstract:
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 spatio-temporal 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.
Citation:
S. A. Gourley, J. W.-H. So, Wu Jian Hong, “Nonlocality of Reaction-Diffusion Equations Induced by Delay: Biological Modeling and Nonlinear Dynamics”, Proceedings of the International Conference on Differential and Functional-Differential Equations — Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11–17 August, 2002). Part 1, CMFD, 1, MAI, M., 2003, 84–120; Journal of Mathematical Sciences, 124:4 (2004), 5119–5153
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