食饵具有Allee效应和集群行为的捕食者-食饵系统动力学行为分析  

Dynamic behavior analysis of a predator-prey system with Allee effect and herd behavior

作　　者：曹奇 杨文生[1,2,3] CAO Qi;YANG Wen-sheng(School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117,China;Fujian Key Laboratory of Mathematical Analysis and Applications,Fuzhou 350117,China;Center for Applied Mathematics of Fujian province(FJNU),Fuzhou 350117,China)

机构地区：[1]福建师范大学数学与统计学院,福建福州350117 [2]福建省分析数学及应用重点实验室,福建福州350117 [3]福建省应用数学中心(福建师范大学),福建福州350117

出　　处：《高校应用数学学报（A辑）》2023年第2期203-213,共11页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11672074);福建省自然科学基金(2022J01192)。

摘　　要：该文考虑了食饵具有Allee效应和一般集群行为的捕食者-食饵模型.文中分析了一定初值条件下种群数量的长时间性态.利用线性稳定性理论讨论了平衡点的局部稳定性,在正平衡点稳定的情况下,讨论了食饵集群行为对捕食者与食饵数量的影响.其次用分支理论给出了系统跨临界分支和Hopf分支存在的条件,利用计算第一Lyapunov系数分析了Hopf分支的方向.最后通过数值模拟验证了结论的可行性.A predator-prey model with prey Allee effect and herd behavior is considered in this paper.The long-term behaviour of the population under certain initial values is analyzed.Then the local stability of all equilibrium points is discussed by using linear stability theory.The effect of the herd behavior on the prey and predator equilibrium densities are discussed in the case of the positive equilibrium point is stable.Next,based on bifurcation theorem,conditions for the existence of Transcritical bifurcation and Hopf bifurcation are derived.The direction of the Hopf bifurcation is analysed by calculating the first Lyapunov number.Finally,numerical simulations are used to verify the feasibility of the conclusions.

关 键 词：ALLEE效应 集群行为 稳定性 HOPF分支 

分 类 号：O175.14[理学—数学]