Two Types Of Functional Response Predator - Predator Model Study Of Periodic Motion

Two classes of predator-prey models of Hollings functional response are discussed in this paper, which are finished using the qualitative analysis and bifurcation theory. And the sufficient conditions are obtained on which limit cycles and bifurcations produced by limit cycles exist. What is more, the periodic motion of these models is analyzed in detail. Four chapters are included in this paper.Chapter one is the introduction. First, the improvement trend and research value are discussed from the point of biological significance and the solution of actual ecological problems. Secondly the main content of this paper and problem are presented. Finally, the definitions and lemmas of qualitative analysis and bifurcation theory are introduced in this chapter, which are used in this paper.A predator-prey model of Holling II functional response is discussed in chapter two. The behavior of the positive equilibriums is analyzed, and the sufficient conditions of nonexistence and existence of limit cycles in system are obtained. Meanwhile, on the condition that parameters satisfy certain conditions, the sufficient conditions are found, on which two or three limit cycles exist at least, according to hopf-bifurcation theory.A predator-prey model of Holling III functional response is discussed in chapter three using the same method as in chapter two. The behavior of positive equilibrium of the model is analyzed, then the sufficient conditions on which the limit cycles in system exist or not are obtained. Additionally, on the condition that the parameters match certain qualifications, the sufficient conditions are found on which two limit cycles exist at least, using hopf-bifurcation theory. Therefore, it makes population dynamics more diverse, but the difficulties of qualitative analysis also increase. At last, a comparison between two classes of predator-prey models of different functional response is made.Algorithm of focus value calculation is presented in chapter four, and besides my personal prospect and work on this thesis is summarized in this chapter.