A Pest Mangement Model1with State Feedback Control

With the development of science and technology, mathematical biology has been widely applied in various fields, such as biological technology, economy, and agriculture. In the past two years, it was found that combined the state-feedback control with biological mathematical models to describe species growth is more practical, which can clearly explain some complex biological phenomena. For example, employing it to study the interaction among population dynamics can favor to understand many pest management issues in the agricultural production. This paper focus on a class of crop pests management models with state-feedback control, which possesses infinite delay in case of weak integral kernel. The models can be modified as a constant system without delay, and the global stability of the positive equilibrium is verified via Bendixson-Dulac criterion. Further, utilized successor function in the geometric theory of ordinary differential equations, it is obtained a sufficient condition for the existence of the order1cycle, and the asymptotical stability of the periodic solution is also proved. The paper includes third sections. First, the research background and significance, research status, and the main work of this paper is presented. Next, some notations and preliminaries are introduced. Finally, the global stability of the positive equilibrium is discussed, and the existence and stability of periodic solution of order1are studied.