Pest Management Models With State Feedback Impulsive Control

Pest management is of great significance to the sustainable development of agriculture and the ecological balance of nature. The minimum losses caused by pests for mankind always catch attention of human. In this paper, combining the pest management and differential equation theory, we discuss the problems related to pest management. The main contents are as follows:First, we mainly introduce the significance, progress and development direction of pest management model with state-feedback impulsive control, and introduce basic knowledge of impulsive differential equation which related to the problem of the research. Finally, we give the main work of this paper.Second, we establish a pest management model with a state-feedback impulsive control, a model which adopts control methods of period spraying pesticides and releasing natural enemies at the moment when the amount of the pests reaches economic threshold. By using the method of characteristics and Dulac theorem, we discuss the existence and stability of equilibrium point without impulse. By using the successor function and Poincaré similarity criteria, we prove the existence and stability of order 1 periodic solution under impulse.Third, we study the pest management model with two state-feed backs impulsive control, a model which adopts control method of releasing natural enemies at the moment when the amount of the pests reaches the smaller economic threshold and period spraying pesticides and releasing natural enemies at the moment when the amount of the pests reaches the larger economic threshold. We study the existence and stability of order 1 periodic solution of the system.Last, we study a class of semi-ratio predator-prey model with pollution-free pest management and impulsive control, a model which adopts control method of period releasing natural enemies at the moment when the amount of the natural enemies decrease to certain threshold. We study the existence and stability of order 1 periodic solution of the system. Numerical simulations are given to illustrate our main results.