The complete classification on a model of two species competition with an inhibitor

Jifa Jiang; Fensidi Tang

doi:10.3934/dcds.2008.20.659

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2008, Volume 20, Issue 3: 659-672. Doi: 10.3934/dcds.2008.20.659

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The complete classification on a model of two species competition with an inhibitor

Jifa Jiang^1, and
Fensidi Tang^2,

1.
Department of Mathematics, Tongji University, Shanghai 200092
2.
Department of Mathematics, University of Science and Technology of China, Hefei 23002

Received: September 30, 2006

Revised: October 31, 2007

Published: August 2008

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Abstract

Hetzer and Shen [3] considered a system of a two-species Lotka-Volterra competition model with an inhibitor, investigated its long-term behavior and proposed two open questions: one is whether the system has a nontrivial periodic solution; the other is whether one of two positive equilibria is non-hyperbolic in the case that the system has exactly two positive equilibria. The goal of this paper is first to give these questions clear answers, then to present a complete classification for its dynamics in terms of coefficients. As a result, all solutions are convergent as $t$ goes to infinity.

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Mathematics Subject Classification: Primary: 34C35; Secondary: 92A15.

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