The Permanence Of Two Types Functional Differential Equations

With the rapid development of modern science and technology, the ecological problems become more and more closely related to human beings. People using the biological model to reflect the ecological laws of biology, but most of these biological models are related to functional differential equations, which includes the periodic solution, stability etc. as its important branches. In the recent twenty or thirty years biological model has made essential and comprehensive progresses and the research results are abundant. The persistent of functional differential equations has attracted many scholars' attention, and has been widely concerned in the academic.This thesis mainly researches on the permanence of two types of functional differential equations: delayed SIR epidemic models and delayed predator - prey model. The thesis is divided into three chapters:The first chapter briefly introduced the development of eco-math, as well as researches which have been carried out on functional differential equations' permanence, and put forward issues to be discussed in this article.Chapter two introduced the meaning and necessity of studying infectious disease model. Focused on permanence of SIR epidemic model, give its definition, durable and some related Lemma theorem and the process of proving. In addition, the thesis has educed the conditions to control and eliminate diseases, proved that the extinction of SIR infectious diseases.Chapter three, simply introduced the background knowledge and current situation of predator - prey biology model. Focused on the permanence of time-delay predator-prey biology model. It firstly introduced its permanence definition and prior knowledge, and then give theorem to the permanence of predator - prey biology model, and to promote the existing literature results.