# American Institute of Mathematical Sciences

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

 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.
Citation: Jifa Jiang, Fensidi Tang. The complete classification on a model of two species competition with an inhibitor. Discrete & Continuous Dynamical Systems - A, 2008, 20 (3) : 659-672. doi: 10.3934/dcds.2008.20.659
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