基于合作捕猎和恐惧效应的捕食-食饵模型定性分析与反馈控制  

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

作　　者：田源 闫鑫蕊 刘艺 TIAN Yuan;YAN Xinrui;LIU Yi(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：《应用数学》2024年第3期840-846,共7页Mathematica Applicata

基　　金：国家自然科学基金项目(11401068)。

摘　　要：在自然界中,种群与种群之间的关系错综复杂.捕食者之间的合作捕猎行为以及食饵对捕食者的恐惧会对种群间的动力学行为带来一定的影响,为此本文研究一类具有合作捕猎和恐惧效应的捕食-食饵模型.首先,建立具有Smith型增长率和恐惧效应以及捕食者合作捕猎的捕食-食饵模型,分析该模型解的存在性与一致有界性,并给出平衡点存在和稳定的条件;其次,通过对捕食者进行控制,建立基于反馈控制的捕食-食饵模型,讨论阶-1周期解的存在性和稳定性;最后,借助于MATLAB进行数值模拟,对以上理论结果进行验证和说明.In nature,the relationships between populations are complex.The cooperative hunting behavior of predators and the fear of predators have certain effects on the dynamic behavior of populations.Therefore,a predator-prey model with cooperative hunting and fear effects is studied in this paper.Firstly,a predator-prey model with Smith type growth rate,fear effect and cooperative predator hunting is established.The existence and uniform boundedness of the solution of the model are analyzed,and the conditions for the existence and stability of the equilibrium point are given.Secondly,by controlling the predator,a predator-prey model based on feedback control is established,and the existence and stability of the order-1 periodic solution are discussed.Finally,the above theoretical results are verified and illustrated through numerical simulation in MATLAB.

关 键 词：反馈控制 合作捕猎 恐惧效应 阶-1周期解 稳定性 

分 类 号：O175[理学—数学]