The dynamical complexity of a Ivlev-type prey–predator system with impulsive effect

Based on the classical predator–prey system with Ivlev-type functional response, an impulsive differential equations to model the process of periodic perturbations on the predator at different fixed time 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, and otherwise, the system can be permanent. Numerical results show that the system considered has more complicated dynamics. such as quasi-periodic oscillation, narrow periodic window, wide periodic window, chaotic bands, symmetry-breaking pitchfork bifurcation and crises, etc.