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Volume 8, Number 2, 2018, Pages 427-442                                                                DOI:10.11948/2018.427
The geometrical analysis of a predator-prey model with multi-state dependent impulses
Jianmei Wang,Huidong Cheng,Yan Li and Xiaoning Zhang
Keywords:Semi-continuous dynamic system, successor function, order one periodic solution, stability.
      Starting from the practical problems of integrated pest management, we establish a predator-prey model for pest control with multi-state dependent impulsive, which adopts two different control methods for two different thresholds. By applying geometry theory of impulsive differential equations and the successor function, we obtain the existence of order one periodic solution. Then the stability of the order one periodic solution is studied by analogue of the Poincar\''{e} criterion. Finally, some numerical simulations are exerted to show the feasibility of the results.
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