基于合作狩猎的捕食者-食饵系统定性分析与反馈控制  

Qualitative Analysis and Feedback Control of Predator-Prey Model Based on Cooperative Hunting Effect

作　　者：田源 李幻梦 TIAN Yuan;LI Huanmeng(School of Science,Dalian Maritime University,Dalian 116026,China)

机构地区：[1]大连海事大学理学院,辽宁大连116026

出　　处：《信阳师范学院学报（自然科学版）》2023年第1期22-27,共6页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11401068);中央高校基本科研业务费(3132022199)。

摘　　要：针对捕食系统中存在的合作狩猎现象,建立了一类具有合作狩猎的捕食者-食饵模型。为了避免特定区域捕食者数量过大导致短时间内食饵资源短缺问题,通过对捕食者群体数量进行限定及控制,建立了基于反馈控制的合作狩猎捕食者-食饵模型。首先,分析了连续系统的动力学行为,讨论了合作狩猎因子对系统正平衡态存在性及稳定性的影响;其次,利用后继函数方法及类Poincaré准则,讨论了反馈控制系统阶1周期解的存在性和稳定性;最后,利用MATLAB进行了数值模拟,对主要研究结果进行了验证。Aiming at the cooperative hunting phenomenon in predator system, a predator-prey model with cooperative hunting is established. In order to avoid the shortage of prey resources in a short time due to the large number of predators in a specific area, a cooperative hunting predator-prey model based on feedback control is established by limiting and controlling the number of predator groups. Firstly, the dynamic behavior of the continuous system is analyzed, and the influence of cooperative hunting factors on the existence and stability of the positive equilibrium state is discussed. Secondly, the existence and stability of order-1 periodic solutions for feedback control systems are discussed by using the method of successor function and analogue of Poincaré criterion. Finally, MATLAB is used for numerical simulation to verify the obtained main research results.

关 键 词：合作狩猎 后继函数 类Poincaré准则 阶1周期解 

分 类 号：O175[理学—数学] Q141[理学—基础数学]