The dynamic complexity of an impulsive Holling II predator–prey model with mutual interference

In this paper we study the dynamic behaviors of an impulsive Holling II predator–prey model with mutual interference. Some sufficient conditions ensuring the prey to be extinct are obtained via the Floquent theory. We also derive some conditions for the permanence of the system by using the comparison method involving multiple Laypunov functions. Finally, the numerical simulation shows that the impulsive system has complex dynamics properties such as quasi-periodic oscillation, narrow periodic window, wide periodic window, chaotic bands, period-doubling bifurcation, symmetry-breaking pitchfork bifurcation, period-halving bifurcation and crises.