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Volume 9,     Number 2,     Summer 2001

 

TWO-PREY ONE-PREDATOR SYSTEM WITH DISCRETE DELAY
RAVINDER KUMAR

Abstract. A Lotka-Volterra model of two competing preys and a predator with discrete time delay due to gestation is considered when it possesses a positive interior equilibrium. Sufficient conditions for its global stability are derived. It is shown that whenever equilibrium in the competition plane is bistable, interior equilibrium for the system cannot be globally stable for at least small and large values of time delay. Further, in this case, persistence cannot occur at least for small values of time delay. A criterion for Hopf bifurcation to occur is given. Conditions for no change in the local stability of the interior equilibrium are obtained.

 

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