Impulsive state feedback control of a predator-prey model

The dynamics of a predator-prey model with impulsive state feedback control, which is described by an autonomous system with impulses, is studied. The sufficient conditions of existence and stability of semi-trivial solution and positive period-1 solution are obtained by using the Poincare map and analogue of the Poincare criterion. The qualitative analysis shows that the positive period-1 solution bifurcates from the semi-trivial solution through a fold bifurcation. The bifurcation diagrams of periodic solutions are obtained by using the Poincare map, and it is shown that a chaotic solution is generated via a cascade of period-doubling bifurcations. (c) 2006 Elsevier B.V. All rights reserved.