Abstract:
A class of predator-prey model with impulsive state feedback control and Allee effect on predator is considered, where the quantity of natural enemies released and the intensity of pesticide sprayed linearly depend on the pest control level. Firstly, the positivity and boundedness on the solutions of uncontrollable system were analyzed, and the sufficient conditions for global asymptotic stability of the positive equilibrium were given. Secondly, the existence of the order-1 periodic solution of the control system was discussed by means of the success function method, and the condition for the stability of the order-1 periodic solution was given. In order to determine the optimal quantity of natural enemies released and the intensity of pesticide sprayed, the optimization model is constructed and analyzed with the aim of minimizing input cost. The results showed that, based on the control strategy proposed, the number of pests can be limited to below an economic threshold and displays periodic variation.