Homoclinic Cycle and Homoclinic Bifurcations of a Predator-Prey Model with Impulsive State Feedback Control

Abstract

In this paper, the homoclinic bifurcation of a predator-prey system with impulsive state feedback control is investigated. By using the geometry theory of semi-continuous dynamic systems, the existences of order-1 homoclinic cycle and order-1 periodic solution are obtained. Then the stability of order-1 periodic solution is studied. At last, an example is presented to illustrate the main results.