Abstract
A mathematical model of two predators competing for a single prey system incorporating population heterogeneity has been proposed and analyzed by extending the system of coupled logistic equations for three species system. The local stability analysis of all the equilibria has been carried out and also globally stable in Varies 2-D planes. Through the analytical results, it is observed that the interior equilibrium of one prey and two competing predators in prey dependent case is always unstable. At the end, discussed the dynamical behavior of a three species interaction with the help of some numerical examples by using MATLAB to support the analytical presentations.
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