Multiple Periodicity And Permanence Of A Delayed Predator-prey Model With Stage Structure

Three delayed predator-prey models with non-monotonic functional response and stage structure are studied. Applying coincidence degree theory, the comparison theorem, and Brouwer fixed point theorem, Multiple periodic solutions, permanence and almost periodic solution of predator-prey models are analyzed, respectively. Our results provide theoretical basis for the development, prediction of population biology. The main works are listed as follows:It is mainly introduced about the historical background and the research progress of biological dynamic system in the first chapter. And some academic achievements on the issue, the shortcomings and the insufficiency of part of the system are analyzed further. Thus the main direction of the research in this paper is derived.In the second chapter, it is mainly studied for the existence of multiple periodic solutions of a delayed predator-prey model with non-monotonic functional response and stage structure. By using coincidence degree theory, the existence of multiple periodic solutions is proven under the some conditions. It can improve the existence of multiple periodic solutions to the model to shorten appropriately environmental cycle. At last, related results are verified by an example.In the third chapter, it is mainly discusses for the permanence of a delayed predator-prey model with non-monotonic functional response and stage structure. By the comparison theorem, the model is permanent under some appropriate conditions. According to the conditions, to control properly the amount of predators can prevent the extinction of prey species effectively.In the fourth chapter, by using the Brouwer fixed point theorem, the sufficient conditions for the existence of a almost periodic solution for the time delay predator-prey model with non-monotonic functional response and stage structure are obtained.The last chapter gives the full text summary and prospect.