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Complex dynamics of one-prey multi-predator system with defensive ability of prey and impulsive biological control on predators. (English) Zbl 1082.92046
Summary: This work investigates the dynamic behavior of a one-prey multi-predator model with defensive ability of the prey by introducing impulsive biological control strategies. By using the Floquet theorem and the small amplitude perturbation method, it is proved that there exists an asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value, and a permanence condition is established via the method of comparison involving multiple Lyapunov functions. It is shown that the multi-predator impulsive control strategy is more effective than the classical one and makes the behavior dynamics of the system more complex.
MSC:
92D40Ecology
34A37Differential equations with impulses
93C95Applications of control theory
34D05Asymptotic stability of ODE
34C60Qualitative investigation and simulation of models (ODE)