Chaotic behavior of a Watt-type predator–prey system with impulsive control strategy

In this paper, by using theories and methods of ecology and ODE, a predator–prey system with Watt-type functional response and impulsive perturbations on the predator is established. It proves that there exists a locally asymptotically stable prey-eradication periodic solution when the impulse period is less than some critical value, otherwise, the system can be permanent. Further, by using the method of computer simulation, the influences of the impulsive perturbations on the inherent oscillation are investigated, which shows the more complex dynamics of the system we considered, such as quasi-periodic oscillation, narrow periodic window, wide periodic window, chaotic bands, period doubling bifurcation, symmetry-breaking pitchfork bifurcation, period-halving bifurcation and crisis, etc. It will be useful for studying the dynamical complexity of ecosystems.