Competing Species With Maturation Delay And Nonlinear Intraspecific Regulation

In this paper, the stage structured competition models with nonlinear intraspecific regulation represented by both discrete and distributed types of delays are proposed and considered. Each species in the discrete delay type model has a corresponding constant maturation time, while in the distributed delay type model, the maturation time of each species obeys some probability distribution. Only the adult members are involved competition and the immature members are in the absence of competition. Dynamical behaviors of the model are studied. And sharp global stability criteria are established for the coexistence equilibrium as well as the extinction equilibrium. Effects of stage structure and nonlinear intraspecific regulation on behaviors of species are also discussed. It is shown that the stage structure of species in both types of systems have negative effect on its permanence and may lead to its extinction through lowering its carrying capacity and surviving degree. But variation of the nonlinear intraspecific regulation parameter of one species can neither destroy its surviving nor completely avoid its extinction, though it may change the surviving or extinction behaviors of its competitor.This paper is organized as follows. In Chapterâ… , we advance two models for discrete and distributed types of delays and consider the equilibria for first model. Then we study the local asymptotic stability of the equilibria in Chapterâ…¡and in Chapterâ…¢, we give three Lemmas and main Theorems of the first model. In the Chapterâ…£we are concerned with the second model and give its main results. The paper ends with a discussion.