Analysis of a Leslie–Gower-type prey–predator model with periodic impulsive perturbations

A modified Leslie–Gower-type prey–predator model with periodic impulsive perturbations is proposed and investigated. It is proved that there exists an asymptotically stable prey-free periodic solution when the impulsive period is less than some critical value. Otherwise, the above system can be permanent. And then the numerical simulations are carried out to study the effects of the impulsive varying parameters of the system. The results of simulations show that the model we consider, under the effects of impulsive perturbations for biologically feasible parametric values, has more complex dynamics including cycle, period adding, 3 T -period oscillation, chaos, period-doubling bifurcation, period-halving bifurcation, period windows, symmetry-breaking pitchfork bifurcation, and non-unique dynamics, meaning that several attractors coexist.