Volume 9, Number 2, Summer 2001
TWO-PREY ONE-PREDATOR SYSTEM WITH DISCRETE DELAY
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.