The geometrical analysis of a predator-prey model with multi-state dependent impulsive

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 Poincaré criterion. Finally, some numerical simulations are exerted to show the feasibility of the results.

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