The Study Of Population Dynamics Behavior With Stage Structure

The particular physiology characteristic that appears in the corresponding stage ofspecies(such as some species only have to birth, to attack prey in their mature stage,etc) are one of the most prevalent phenomena of nature, and become one of the mostinterested contents for many scholars no matter in domestic and international scope. Inthis paper, based on the study of other authors, we give a more depth and aborad researchabout some predator-prey systems with stage-structure, which include: periodic solutionfor a nonautonomous stage-structured predator-prey model with time delay; periodicsolution and its stability of a nonautonomous predator-prey system with stage-structureand double time delays.The main contents of this paper can be summarized as follows:1. In section 1, firstly, we introduce the ecological background of this paper; secondly,some newly important research conclusion about single systems and predator-prey systemswith stage-structure and time delay are presented; finally we give our research model.2. In section 2, a nonautonomous stage-structured predator-prey model with timedelay is studied. By using the continuation theorem of coincidence degree theory andsome analysis methods, su?cient conditions about the existence of a positive periodicsolution for the system is established.3. In section 3, we study a periodic nonautonomous predator-prey system with stage-structure and double time delays. Some su?cient conditions on the existence, uniquenessand globally asymptotically stable of periodic solution are established by applying thesame strategy used in section 2 and constructing appropriate Lyapunov function.Finally, Our numerical simulation shows that the results we obtained in this paperby mathematical analysis are e?ective and feasible, and, it is very meaningful for studyingthe periodic stage-structured system from actual ecological background.