American Institute of Mathematical Sciences

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July  2008, 20(3): 659-672. doi: 10.3934/dcds.2008.20.659

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, China
2. 

Department of Mathematics, University of Science and Technology of China, Hefei 23002, China

Received  October 2006 Revised  November 2007 Published  December 2007

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.
Keywords: strong monotonicity, inhibitor, convergence, Lotka-Volterra two species competition, nonexistence for periodic solutions.
Mathematics Subject Classification: Primary: 34C35; Secondary: 92A1.
Citation: Jifa Jiang, Fensidi Tang. The complete classification on a model of two species competition with an inhibitor. Discrete and Continuous Dynamical Systems, 2008, 20 (3) : 659-672. doi: 10.3934/dcds.2008.20.659
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