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The study of predator–prey system with defensive ability of prey and impulsive perturbations on the predator. (English) Zbl 1081.34041
A predator-prey system with nonmonotonic functional response and impulsive perturbations on the predator is considered. By using Floquet’s theorem and the method of small amplitude perturbation, a locally asymptotically stable prey-eradication periodic solution is established when the impulsive period is less than some critical value. Otherwise, if the impulsive period is larger than the critical value, the system is permanent. Further, using numerical simulations, the influences of the impulsive perturbations on the inherent oscillation are investigated. With increasing impulsive value, the system displays a series of complex phenomena, which include (1) quasi-periodic oscillating, (2) period-doubling, (3) period-halfing, (4) nonunique dynamics (meaning that several attractors coexist), (5) attractor crisis and (6) chaotic bands with periodic windows.
MSC:
34C60Qualitative investigation and simulation of models (ODE)
92D25Population dynamics (general)
34A37Differential equations with impulses
34C25Periodic solutions of ODE
34D05Asymptotic stability of ODE
34D20Stability of ODE
34C23Bifurcation (ODE)
34C28Complex behavior, chaotic systems (ODE)