摘要
建立了食饵具有Allee效应的捕食模型,讨论了系统的有界性和平衡点的存在性.并证明了平衡点的局部渐近稳定性,进而通过构造Lyapunov函数分析了正平衡点的全局渐近稳定性,利用数值模拟讨论了Allee效应对系统的影响:Allee效应是系统的不稳定因素.
We consider the predator-prey system with Allee effect for the prey,study the boundedness of the system and the existence of the equilibria.We obtain the sufficient conditions of locally asymptotically stability of the equilibria.Furthermore,we analyze the global stability of the positive equilibria by Lyapunov method and discuss the Allee effect on the system by numerical simulations.The Allee effect is the unsteady factor of system.
出处
《数学的实践与认识》
CSCD
北大核心
2013年第20期245-249,共5页
Mathematics in Practice and Theory
基金
甘肃省自然科学基金(1010RJZA127
1208RJZA186)
国家支撑项目(2007BAD88B07)
关键词
ALLEE效应
捕食模型
稳定性
Allee effect
predator-prey system
stability analysis