Existence Of Positive Periodic Solutions For Impulsive Population Models

In nature,the occurrence of many life phenomena and the optimal control and man-agement of populations are not a continuous process and cannot be described simply by differential equations or difference equations.Therefore,as a special discontinuous sys-tem,the pulse differential system is widely used to analyze the changes of the population quantity in biological mathematics and to explain the objective phenomena.The behavior of population dynamics can help us better understand the natural population changes and explain complex biological phenomena.In this thesis,by using Mawhin's continuation theorem,we study the existence of positive periodic solutions for several kinds of popu-lation models with impulses and different functional response functions.The full text is divided into four chapters,the specific contents are arranged as follows:Chapter one mainly introduces the research background,research status,the main work and innovation of this paper.In chapter two,firstly,we consider a neutral predator-prey model with impulsive and Holling ? ratio-dependent predator-prey models,under the condition that the time delay of the neutral term is less than or equal to zero.Secondly,Lotka-Volterra predator-prey model with impulsive delays is discussed.By using Mawhin's continuation theorem,the existence of positive periodic solutions is obtained.In chapter three,we study the predator-prey model with time delay under the influence of impulsive and neutral terms,and apply Mawhin's continuation theorem to obtain the existence of multiple positive periodic solutions.In chapter four,we summarize the main work of this paper and look forward to future research.