一类具有状态依赖脉冲影响的捕食者-食饵模型动力学分析  

Dynamic Analysis of a Predator-Prey Model with State-Dependent Impulsive Effects

作　　者：李永凤 朱城志 刘艳伟 LI Yong-feng;ZHU Cheng-zhi;LIU Yan-wei(School of Mathematics and Information Science,Zhengzhou University of Light Industry,Zhengzhou 450002,China)

机构地区：[1]School of Mathematics and Information Science,Zhengzhou University of Light Industry,Zhengzhou 450002,China

出　　处：《Chinese Quarterly Journal of Mathematics》2023年第1期1-19,共19页数学季刊（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 11901541);The Scientific and Technological Key Projects of Henan Province (Grant No. 202102310631);The Key Scientific Research Project in Colleges and Universities of Henan Province of China (Grant No. 19A110036)

摘　　要：In this paper, a pest-dependent model and integrated pest management strategy is proposed, that is, when pest populations reach levels that impair economic development, we will use a combination of strategies, such as biological, cultural and chemical control strategies reduce pests to a reasonable level. First, we investigated the system without control measures, and discussed the existence and stability of equilibria,we also proved the system has no limit cycle. Then, a state feedback impulsive model is constructed, the existence and uniqueness of the order-one periodic solution are proved by means of the successor function method to confirm the feasibility of the biological and chemical control strategy of pest management. Secondly, the stability of system is proved by the analogue of the Poincar’e criterion. Finally, we give an example and numerical simulations to explain the mathematical conclusions.

关 键 词：Predator-prey model State feedback Period solution Stability 

分 类 号：O187.1[理学—数学]