Geometric analysis of a pest management model with Holling’s type III functional response and nonlinear state feedback control

In this paper, based on a predator–prey model with Holling’s type III functional response, a pest management system with artificial interference is proposed. We assume that the artificial interference strategy will be taken to control pests when their number reaches a certain threshold. Based on this assumption, the artificial interference strategy of the system with nonlinear state feedback control is analyzed by using the geometric theory of ordinary differential equations. We first study the existence of periodic solutions of the model by successor functions and then the stability of periodic solutions. Finally, numerical simulations are given to illustrate our theoretic conclusions.

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