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Dynamics of an impulsively controlled Michaelis-Menten type predator-prey system. (English) Zbl 1221.34031
Summary: We study a predator–prey system with a Michaelis–Menten functional response and impulsive perturbations which contain chemical and biological control terms. By applying the Floquet theory, we establish conditions for the existence and stability of prey-free solutions of the system. We also show the existence of a positive periodic solution of the system by using the bifurcation theorem and find a sufficient condition that makes the system permanent. Moreover, numerical results on impulsive perturbations show that the system we consider can give birth to various kinds of dynamical behaviors.
MSC:
34A37Differential equations with impulses
34D20Stability of ODE
92D25Population dynamics (general)
93C15Control systems governed by ODE
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