The dynamical complexity of a predator–prey system with Hassell–Varley functional response and impulsive effect

In this paper, the dynamics of an impulsively controlled predator–prey system with the Hassell–Varley functional response are studied. Under impulsive control, the conditions for the existence of a stable prey-free solution and for the permanence of the system are investigated by using Floquet theory and comparison theorems. Also the existence of a nontrivial periodic solution under some conditions is shown via the bifurcation theorem. Finally, numerical simulations are given to substantiate our theoretical results and to illustrate various dynamical behaviors of the system.