Multi-cycle Of A Class Of Ecosystem Change Parameter α (t) Of The Phased Construction Of The Solution

In this paper, we investigate a non-autonomous stage-structured Holling II type function response model with a changing parameter a(t) and multiple harvesting terms. By using coincidence degree theory, we establish the existence of Multiple positive periodic solutions for the above model. A brief description of the organization of the thesis is as follows.In chapter1, we made an overview of the selection background, the research status of its periodic solution and the existing achievements.In chapter2, coincidence degree theory, as well as other functional analysis of the basic knowledge (such as Banach space, isomorphic mapping, Fredholm mapping definitions and their related knowledges, Arzela-Ascoli theorem and Topological Degree theory etc.) which are related to this article are reviewed.In chapter3, by using coincidence degree theory and other functional anal-ysis knowledges, we study the existence of multiple periodic solutions of stage-structured, ratio-dependent Holling II type functional response system with varying parameter a(t) and harvesting terms.In chapter4, in order to illustrate the results of chapter3, we give a concrete biological model example.In chapter5, we summarize this article and put forward the direction of the efforts in the future.