Convergence in competition models with small diffusion coefficients

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:211

Article

Hutson, V ; Lou, Y ; Mischaikow, K

关键词: reaction-diffusion;    competing species;    spatial inhomogeneity;    small diffusion limit;    asymptotic dynamics;   

DOI  :  10.1016/j.jde.2004.06.003

来源: Elsevier

【 摘 要 】

It is well known that for reaction-diffusion 2-species Lotka-Volterra competition models with spatially independent reaction terms, global stability of an equilibrium for the reaction system implies global stability for the reaction-diffusion system. This is not in general true for spatially inhomogeneous models, We show here that for an important range of such models, for small enough diffusion coefficients, global convergence to an equilibrium holds for the reaction-diffusion system, if for each point in space the reaction system has a globally attracting hyperbolic equilibrium. This work is planned as an initial step towards understanding the connection between the asymptotics of reaction-diffusion systems with small diffusion coefficients and that of the corresponding reaction systems. (c) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free