Qualitative analysis of a predator-prey system with mutual interference and impulsive state feedback control.

*(English)*Zbl 1384.92050Summary: In this paper, a predator-prey system with mutual interference and impulsive state feedback control is constructed. Firstly, by using the stability theorem, we obtain the global asymptotically stability of the positive equilibrium for the system without impulse effects. Secondly, by using the geometric theory of differential equations, the method of successor functions and mathematical analysis, we obtain some sufficient conditions for the existence, uniqueness and orbital asymptotically stability of the order-1 periodic solution for the system with impulse effects. Finally, the main conclusions are verified by numerical simulation, and the pest prevention and control strategies on combining light trapping and water-gun spraying are proposed.

##### Keywords:

impulsive state feedback control; successor function; order-1 periodic solution; orbital asymptotically stable; pest prevention and control
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\textit{Z. Liang} et al., Nonlinear Dyn. 87, No. 3, 1495--1509 (2017; Zbl 1384.92050)

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