Qualitative Analysis For A Class Of Predator-Prey Model

Consider a Leslie-Gower and Holling-type II predator-prey model and model with state dependent impulsive effects where a1,a2, b, h, ki,k2, r1 and r2 are positive constants, p ∈(-1,00),q E (0,1).Chapter 1 introduces the background and the method of research.In Chapter 2, boundedness of system (1) is proved by using theory of differential inequalities and a attractive set of (1) is given. The results revise the correspond-ing those in literature [M. A. Aziz-Alaoui, M. Daher Okiye, Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes, Appl. Math. Lett.2003,16:1069-1075].In Chapter 3, existence of positive equilibria of (1) is discussed. New sufficient conditions for global asymptotical stability of positive equilibria is obtained by Lay-punov method.In Chapter 4, existence of semi-trivial periodic solution of model (2) is obtained by step method and sufficient condition for stability of the semi-trivial periodic solution is obtained by Poincare map. The results which extend the corresponding ones of [Linfei Nie, Zhidong Teng, Lin Hu, Jigen Peng, Qualitative analysis of a modified Leslie-Gower and Holling-type II predator-prey model with state dependent impulsive effects, Nonlinear Analysis:Real World Applications,2010,11:1364-1373] to model (2) are new.