摘要
This paper concerns the growth of two predator species competing exploitatively for the same prey population. The prey are assumed to regenerate in the absence of predation by logistic growth. The predators are assumed to feed on the prey with a saturating functional reponse to prey density. Specifically, we assume that Michaelis–Menten kinetics or the Holling “disc” model describe how feeding rates and birth rates change with increasing prey density. We focus on the question as to when the competitive exclusion principal holds, given the growth parameters of the prey and the functional response parameters of the two predators. Which predator wins or loses depends critically on the relative magnitude of the prey carrying capacity, K, and the $\\\\\\\\\\\\\\\\lambda $ parameters of the two predators. (The parameter $\\\\\\\\\\\\\\\\lambda _i $ is the ratio of the ith predator’s Michaelis–Menten (half-saturation) constant to its intrinsic rate of increase, times its death rate.) Coexistence for the predators also appears possible for a wide range of parameters.