Impulsive state feedback control of predator-prey system with Hassell-Varley functional response

In this paper, the dynamics of an impulsively controlled predator-prey system with the Hassell-Varley functional response are studied. Based on classical continuous theorem of coincidence degree and skillful analysis techniques, some sufficient and necessary criteria for the existence of positive periodic solutions are derived, which are used to generate impulsive control strategy to excite or remove the periodic oscillation in this system. Under impulsive control, numerical simulations are given to substantiate our theoretical results and to illustrate various dynamical behaviors of the system.