On The Number Of Periodic Solutions Of Delay Differential Equations

For the study of delay differential equations,a large number of scholars at home and abroad have studied the existence and number of periodic solutions.For every type of delay differential equations,the research methods may not be same and each method has its own unique advantages.Among them,the Kaplan-Yorke method is the most fundamental way to study delay differential equations.Now,more and more scholars have applied more effective methods to study different kinds of delay differential equations based on the Kaplan-Yorke method.In this paper,we consider the existence and number of periodic solutions for a class of delay differential equations with the form x(t)= bx(t-1)+ ?f(x(t),x(t-1),?),based on the Kaplan-Yorke's method.Especially we consider a kind of delay differential equations with f a polynomial having parameters and find the number of periodic solutions with period 4/4k+1 or 4/4k+3.In chapter one,we are mainly introduces the source of the research topic and the present research situation.Also,we will introduces the methods we use in this article and describe a novel results.In chapter two,we introduce some basic knowledge,some theoretical knowledge and the theoretical basis would be used in our article.we will combine previous research results to pave the way for our research.In chapter three,we explore the existence and number of periodic solutions for a class of delay differential equations,Based on the Kaplan-Yorke method and applied bifurcation theory,then we will study the influence of disturbance on periodic solutions.In chapter four,we will give a specific application of the theorems,Also,we will verify the correctness of the results by calculation of the specific cases.