A Cydia Pomonella Integrated Management Predator-Prey Model with Smith Growth and Linear Feedback Control

Abstract

Cydia Pomonella has great influence on the output and quality of apple, therefore, it is an interesting subject to find out the optimum control strategy of Cydia Pomonella. A Cydia Pomonella integrated management predator-prey model with Smith growth and linear feedback control is established in this paper, and the pulse parameter linearity is dependent on controlling level. Firstly, we prove the existence and uniqueness of order one periodic solution (OOPS) by using differential equation geometry theory and successor function method. Secondly, the stability of OOPS is proved by using the geometric method. Finally, with the discussion of different parameters, we verify the theoretical results by numerical simulations, and demonstrate the advantages and disadvantages of biological control strategy, chemical control strategy and integrated control strategy. Moreover, the optimization model with minimum cost is established by using OOPS and optimal control level of the model is obtained.