Study On The Existence Of Two Nonlinear Models Periodic Or Almost Periodic Solutions

This paper deals with two class of ecological models,by using Mawhin's contin-uation theorem to derive the necessary conditions for the existence of multiple positive or periodic solutions.This article is organized as follows:In the first chapter,we introduce the background and significance of the topic briefly,and present the research status and preliminary knowledge.In the second chapter,we mainly study when the external environment pollution or biological toxins affect the food chain system,by using coincidence degree continu-ation theorem to study the existence of almost periodic solutions for a class of n species food chain system in the pollution environment,we mainly use the Mawhin's coinci-dence degree continuation theorem to deduce the necessary conditions for the existence of multiple positive almost periodic solutions,we gain that the system at least has 2~n almost periodic solutions and generalize the conclusions of almost periodic solution of food chain with pollution-free parameters in the past,we also get some new existence criteria at the same time.In the third chapter,we discuss when the new infectious diseases spreading in the ecosystem and need to master the balance and control of the infectious diseases,by using the coincidence degree continuation theorem to discuss the positive periodic solutions for a class of nonautonomous SIQR epidemic model with periodic infection rate,we obtain the necessary conditions for the stochastic system which has at least one periodic solution.In the fourth chapter,we make a brief summary of the full text and review,and make a prospect for the next step of the research issues.