Global asymptotic behavior in a Lotka–Volterra competition system with spatio-temporal delays

Jia-Fang Zhang and Heshan Chen

Chaos, Solitons & Fractals, 2014, vol. 61, issue C, 69-75

Abstract: This paper is concerned with a Lotka–Volterra competition system with spatio-temporal delays. By using the linearization method, we show the local asymptotic behavior of the nonnegative steady-state solutions. Especially, the global asymptotic stability of the positive steady-state solution is investigated by the method of upper and lower solutions. The result of global asymptotic stability implies that the system has no nonconstant positive steady-state solution.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:61:y:2014:i:c:p:69-75

DOI: 10.1016/j.chaos.2014.03.001

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