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Periodic solution of a Leslie predator-prey system with ratio-dependent and state impulsive feedback control. (English) Zbl 1377.37117
Summary: In this paper, a Leslie predator-prey system with ratio-dependent and state impulsive feedback control is investigated by applying the geometry theory of differential equation. When the economic threshold level is under the positive equilibrium, the existence, uniqueness and orbital asymptotical stability of order-1 periodic solution for the system can be obtained. When the economic threshold level is above the positive equilibrium, and the positive equilibrium is a focus point, sufficient conditions of the existence, uniqueness and orbital asymptotical stability of order-1 periodic solution for the system are also acquired. Furthermore, when the positive equilibrium is an unstable focus point, the existence of order-1 periodic solution of the impulsive system can be obtained within limit cycle of the continuous system. The mathematical results can be verified by numerical simulations.

MSC:
37N25 Dynamical systems in biology
92D25 Population dynamics (general)
93B52 Feedback control
34A37 Ordinary differential equations with impulses
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