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Volume 2,     Number 2,     Spring 1994

 

PERSISTENCE AND EXTINCTION IN A
COMPETITION-DIFFUSION SYSTEM
WITH TIME DELAYS
XIN LU

Abstract. A class of time-delay reaction-diffusion systems which arise from the model of two competing ecological species is discussed. We study, in this paper, the global attractivity of the positive steady states in terms of the natural growth rates of the species. Through a monotone iterative scheme, it is proven that when the natural growth rates are in certain unbounded parameter sets, the time-delay reactiondiffusion system has a positive global attractor enclosed by positive steady-state solutions. Asymptotic stability of the trivial and semi-trivial steady states are obtained explicitly. These persistence and extinction results are also demonstrated numerically.

 

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