Qualitative Analysis Of The Predator-prey Models With Functional Response

In this thesis, by using the determinant of Jacobian, comparison theorem, Lyapunov function and continuation theorem, etc, several predator-prey systems with func-tional response were studied for its stability and periodic solutions.The thesis is divided into three sections.Chapter1studies the predator-prey model with Michaelis-Menten type func-tional response and continuous threshold harvesting we obtain the existence of equilibriums, and estimate the stability of the equilib-riums by the determinant of Jacobian.Chapter2studies a mutual interference predator-prey model with Holling III functional response By using the comparison theorem and establishing proper Lyapunov function, we obtain the sufficient conditions of permanence and global asymptomatic stability.Chapter3studies a neutral predator-prey model with Beddington-DeAngelis functional response and harvesting By using continuation theorem and establishing proper Lyapunov function, we obtain the existence and uniquness of positive periodic solutions.