A Nonautonomous Predator-prey System With Stage Structure

The majority of populations have a process of growing up, and in the different stages,they will show different characteristics and we can easily find a notable difference in theireach physiology function. Therefore, according to the characteristics of the populations,dividing the living beings into several stages to build the model then doing the research sothat we can truly reflect reality. This paper mainly discussed the persistence of anonautonomous predator-prey system with stage structure as following:Introducing stage structure to the nonautonomous predator-prey system, we constructthe system with Holling IV and B-D functional response. Among the nonautonomouspredator-prey system with stage structure, we consider the influence of prey supplement onthe population continued survival. At the same time, for the protection of endangeredspecies, for the human and the nature harmonious development, it also has a positivemeaning. We get the sufficient conditions for the uniform persistence of the system and theexistence and uniqueness of the period solution which corresponding the period system andglobal asymptotic stability.For the nonautonomous predator-prey system with stage structure, we consider theinfluence of time delay on the population continued survival. We build the nonautonomouspredator-prey system with stage structure and time delay which is development of theabove model. We obtain the sufficient conditions for the survival of the populations andthe existence of the period solution which is the part of the period system.Introducing Holling IV or BD functional response to above predator-prey system, westudy the continued survival of the populations. For the populations which growth periodlonger, by introducing the effect of time delay and building an predator-prey system withtime delay effect, we study the effect of time delay on continued survival for thepopulation which growth period longer. The predator-prey system with stage structuredetailing the description of present situation of the population living environment,enriching the biological population theory, effectively protecting the species, safeguardingbiodiversity and maintaining ecological balance provides theory basis for human. By introducing time delay and prey supplement, aiming at the study of the stage structure,making people understand the changing and developing laws of the continued survivalbetween the populations, so that they can take corresponding counter measures to thedifferent living environment, effectively maintain biodiversity and especially provideeffective ways to protect endangered species.