The Study For Two Species Dynamics Models With Stage-structure

In nature world, as the limitation of space and natural resources, any specie's existence and extinction is affected by others. As for meat animals, the source of food is else living things. It forms the relation of prey-predator. In the same living space, the population's existence and extinction have restrain effect on other species. It forms the relation of competition. So the phenomenon of predation and competition are common.In the real world, the stage-structure of immaturity and maturity is present in all animals. On each physiological stage, its characteristic has obvious difference. So only we build the model by dividing it into several stages, we can really reflect the reality.In recent years, the prey-predator models and competition models with stage-structure have historically been concerned and researched by many ecologists. Basis of existing results and some types of predation and competition, it establishes two-species dynamics models with stage structure.This article applies the ordinary differential equations, such as the Lyapunov function method, comparison theorem, the theory of coincidence degree of continuity theorem, fixed point theorem, the limit method, to obtain the sufficient conditions for the sustained persistence, the global asymptotic stability, periodic solutions and almost periodic solutions. It provides some guidance for the continued persistence of biological species.This article's research works mainly have the following two aspects:(1)The two-species prey-predator models with Holling type response and stage structureIn the second chapter, in the first section a two-species model with Hollingâ…¢functional response and stage structure is proposed, the paper gives the sufficient conditions of the uniform persistence and the global asymptotic stability of the positive periodic solution.In the second section, it discusses the existence of the predator system's periodic solution with cannibalism and Hollingâ…¡functional response. In the third section, the model considers the delay factor and the necessary and sufficient condition is derived.(2)The two-species competition models with time-delay and stage structureIn the third chapter, a general two-species competition model with time-delay and stage structure is built and the equilibrium points of the model are qualitative analyzed in the first section. In the second section, the mixed model combing predation with competition is proposed, the sufficient conditions for the uniquely existence and global asymptotic stability of its periodic solution and almost periodic solution are obtained.