Vibration Of The Second-order Nonlinear Impulsive Differential Equations And Solution Of Discrete Ecosystem State

This paper is mainly devoted to investigate a difference equation and the asymptotic behaviors of solutions of a discrete ecological system. In the first chapter, we study the oscillation of a second order nonlinear impulsive difference equation. In the second chapter, firstly, we study the persistence of a predator-prey discrete system of three species with HollingⅡfunctional response, then, sufficient conditions are obtained for the existence and global stability of positive periodic solution of this system by using the technique of Mawhin continuation theorem and constructing discrete Lyapunov function.