The Problem of Periodic Solutions for pLaplacian Neutral Functional Differential Equation and Ratiodependent Predatorprey System 

Author  DongRanRan 
Tutor  YanPing 
School  Anhui Normal University 
Course  Applied Mathematics 
Keywords  Periodic solutions Neutral Rayleigh equation Deviating argument Predatorprey system Ratiodependence BeddingtonDeAngelisfunctional response 
CLC  O175 
Type  Master's thesis 
Year  2012 
Downloads  16 
Quotes  0 
Behavior of the solutions is a basic problem of diferential equationstheory, its an important aspect is ascertaining the existence of periodicsolutions for equations or system and under what conditions exist periodic solution. This has been considered by many scholars.In this paper, a ratiodependent predatorprey system and apLaplacian neutral Rayleigh equation are researched. we obtian the existence of periodic solutions of them by using the theory of coincidence degree and extension of Mawhin’s continuation theorem respectively. Thisdissertation is divied into four chapters.In the first chapter, we introduce the background of ratiodependentpredatorprey system and the development situation of neutral functionaldiferential equation, covering the content, related concepts and lemmas.In the second chapter, by using extension of Mawhin’s continuationtheorem, we study the existence of periodic solutions to apLaplacianneutral Rayleigh equation with deviating arguments.In the third chapter, we investigate a ratiodependent threespeciespredatorprey system with the BeddingtonDeAngelis functional response,and use coincidence degree theory to prove that it exists periodic solutions.In the fourth chapter, the research content is summarized and futureprospect is put forward.