Nonlinear diffusion and stable period 2 solutions of a discrete reaction-diffusion model
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摘要
A discrete form of a nonlinear parabolic equation is considered. This equation is in fact a model for migrating populations, and contains a quadratic reaction term, and a diffusion term which can be either linear for nonlinear. Attention is focused on the case of nonlinera diffusion, and in particular period 2 solutions of the discrete version. Conditions for the existence and stability of two types of period 2 solutions are determined analytically. These analytical results, which are local in the neighborhood of fixed points, are compared with the results of some numerical experiments, showing that one of these period 2 solutions is a considerably stronger attractor than the other.
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论文评审过程:Received 1 June 1988, Revised 5 September 1988, Available online 21 March 2002.
论文官网地址:https://doi.org/10.1016/0377-0427(89)90039-3