The dynamics of a Prey-Predator model with impulsive state feedback control

The dynamics of a prey-predator model with impulsive state feedback control is studied by an autonomous system with impulses. The dynamical behavior of this system is discussed by means of both theoretical and numerical ways. The sufficient conditions of existence and stability of the semi-trivial periodic solution, positive period-one, and positive period-two solutions are obtained by using Lambert W function and the analogue of the Poincaré criterion. The bifurcation analysis shows that solutions appear via a cascade of period-doubling in some interval of parameters. The bifurcation diagrams, the Lyapunov exponents, and the phase portraits are given in two examples. The discussion of prey (pest) control strategy shows that the impulsive state feedback control is effective.