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The dynamical complexity of a Ivlev-type prey-predator system with impulsive effect. (English) Zbl 1152.34310

Summary: 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.

MSC:

34A37 Ordinary differential equations with impulses
34D05 Asymptotic properties of solutions to ordinary differential equations
37N25 Dynamical systems in biology
92D25 Population dynamics (general)
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