Complex dynamics of a Holling type II prey–predator system with state feedback control

Abstract

Abstract The complex dynamics of a Holling type II prey–predator system with impulsive state feedback control is studied in both theoretical and numerical ways. The sufficient conditions for the existence and stability of semi-trivial and positive periodic solutions are obtained by using the Poincare map and the analogue of the Poincare criterion. The qualitative analysis shows that the positive periodic solution bifurcates from the semi-trivial solution through a fold bifurcation. The bifurcation diagrams, Lyapunov exponents, and phase portraits are illustrated by an example, in which the chaotic solutions appear via a cascade of period-doubling bifurcations. The superiority of the state feedback control strategy is also discussed.