American Institute of Mathematical Sciences

July  2009, 23(3): 1041-1060. doi: 10.3934/dcds.2009.23.1041

A discretization scheme for an one-dimensional reaction-diffusion equation with delay and its dynamics

 1 Departamento de Ciências Exatas, Universidade Federal de Lavras, Lavras, MG, Brazil 2 Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, SP, Brazil

Received  December 2007 Revised  September 2008 Published  November 2008

The goal of this paper is to present an approximation scheme for a reaction-diffusion equation with finite delay, which has been used as a model to study the evolution of a population with density distribution $u$, in such a way that the resulting finite dimensional ordinary differential system contains the same asymptotic dynamics as the reaction-diffusion equation.
Citation: Maria do Carmo Pacheco de Toledo, Sergio Muniz Oliva. A discretization scheme for an one-dimensional reaction-diffusion equation with delay and its dynamics. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 1041-1060. doi: 10.3934/dcds.2009.23.1041
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