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Extinction and permanence of a three-species Lotka-Volterra system with impulsive control strategies. (English) Zbl 1167.34350
Summary: A three-species Lotka-Volterra system with impulsive control strategies containing the biological control (the constant impulse) and the chemical control (the proportional impulse) with the same period, but not simultaneously, is investigated. By applying the Floquet theory of impulsive differential equation and small amplitude perturbation techniques to the system, we find conditions for local and global stabilities of a lower-level prey and top-predator free periodic solution of the system. In addition, it is shown that the system is permanent under some conditions by using comparison results of impulsive differential inequalities. We also give a numerical example that seems to indicate the existence of chaotic behavior.

MSC:
34C60Qualitative investigation and simulation of models (ODE)
34A37Differential equations with impulses
34C25Periodic solutions of ODE
34D20Stability of ODE
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