具有强Allee效应及Holling-Ⅱ型反应项的捕食-食饵模型的全局分歧解及其稳定性  

Existence and stability of solutions for predator-prey model with strong Allee effect and Holling-Ⅱ functional response

作　　者：冯孝周[1] 孙素平 戴志敏[1] FENG Xiao-zhou;SUN Su-ping;DAI Zhi-min(College of Science,Xi'an Technological University,Xi'an 710032,Shaanxi,China)

机构地区：[1]西安工业大学理学院,陕西西安710032

出　　处：《西北师范大学学报（自然科学版）》2018年第2期6-12,共7页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(61102144);陕西省自然科学基金资助项目(2013JC2-31);陕西省教育厅专项科研计划资助项目(14JK1353);西安工业大学研究生教改项目(2017033);西安工业大学校长基金资助项目(XAGDXJJ17028)

摘　　要：研究一类具有强Allee效应和Holling-Ⅱ型功能反应项的捕食-食饵模型解的存在性、分歧和稳定性.首先运用极值原理得到了系统正平衡态解的先验估计;然后以捕食者的死亡率为分歧参数,利用分歧理论和Leray-Schauder度理论,得到了半平凡解处的局部分歧解的存在性;将局部分歧解延拓为全局分歧后讨论了局部分歧解的稳定性.The existence,bifurcation and stability of positive steady-state solutions to the prey-predator model with strong Allee effect and Holling-Ⅱresponse function are discussed.First,some priori estimates of positive steady-state solutions is given by means of the maximum principle.Then taking the death rate of predator as a bifurcation parameter,the existence of local bifurcation from semi-trivial solutions is observed by using bifurcation theory and Leray-Schauder degree theory,and the local bifurcation is extended to global bifurcation.Finally,the stability of the local bifurcation solution is also discussed.

关 键 词：捕食-食饵模型 强Allee效应 分歧理论 稳定性 

分 类 号：O175.25[理学—数学]