Impulsive periodic oscillation for a predator–prey model with Hassell–Varley–Holling functional response

This paper considers impulsive periodic oscillation in a predator–prey model with Hassell–Varley–Holling functional response. Based on classical continuous theorem of coincidence degree and skilful 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. We give some numerical examples to illustrate main results and present some interesting problems.