The Mathematical Model Of Two Specie Groups Competition With An Inhihitor

This paper deals with the mathematical model of twospecie-groups competition with an inhibitor. Firstly, we consider thestability for boundary equilibria, then prove that this system has at mosttwo positive equilibria, and both positive equilibria are hyperbolic ifthere are two positive equilibria. On the basis of these conclusions, wediscuss the global behavior when it has exactly two positive equilibria indetail, and find two cases different from that in3-dimensional system.We also discuss the classification of dynamics for the global behavior interms of coefficients when there is a unique positive equilibrium. Finally,we show that the inhibitor parameter exercises a great influence on thenumber of equilibria, and several examples will be given in the casethere are two positive equilibria or a unique positive equilibrium.