Contribution to Competing Species Modeling with Distributed Delay

Abstract

In this paper a competing species model is analyzed taking into account the seminal paper of Hsu, Hubbell and Waltman (1978), where two predators compete for a common prey without interference between rivals. Here a distributed delay is introduced in each one of the equations of the predator populations in the same way as suggested by Wolkowicz, Xia & Ruan (1997), in order to model the conversion time lag of consumed prey biomass into predator biomass. Using the linear trick chain technique, the solutions are analyzed from an “equivalent system” of ordinary differential equations looking to answer under what conditions will neither, one, or both species of predator populations survive, giving the appropriate insight of the biological point of view.