Dynamical analysis of a pest management Leslie–Gower model with ratio-dependent functional response

Agricultural pests are great threat for agricultural production, and the development of effective pest control methods is becoming an interesting topic and attracts great attentions. In this work, an integrated pest management model with Leslie–Gower type and ratio-dependent functional response is investigated, and the sufficient conditions for the existence and stability of the order-1 periodic solution are obtained by applying successor function method and analogue of Poincaré criterion. Meanwhile, a cost minimization model by means of the order-1 periodic solution is formulated to determine the optimal control level. The theoretical results are verified by computer simulations for two specified models, and it indicates that the proposed control strategy could keep the pest below the economic level. In addition, to verify the complex dynamics of the proposed model, an order-2 periodic solution and an order-3 periodic solution are obtained by adjusting one key control parameter in the simulations.

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