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Volume 2,     Number 2,     Spring 1994

 

BOUNDEDNESS AND PERSISTENCE OF A
DELAYED PREDATOR-PREY MODEL WITH
ALMOST PERIODIC CARRYING CAPACITY
HSIN CHU AND LI QIANG

Abstract. In this paper a delayed Gause-type predator-prey model with almost periodic carrying capacity is proposed. We observe that a critical vector function (u*,v*(t)), which is the positive equilibrium if the carrying capacity is a constant, plays an important role in this model and characterizes the relative change rates of the populations. With the help of this function, we are able to obtain sufficient conditions for boundedness and persistence of the model. Our persistence criterion coincides with the one proposed by Gatica and So for the case without delay. Therefore, the incorporation of delays to the ODE models does not alter persistence.

 

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