一类具有时滞和HollingⅡ类功能反应的捕食者-食饵模型  

A predator-prey model with functional response and time-delay

作　　者：唐贵坚[1] 唐清干[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2012年第5期402-405,共4页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(11061010);广西自然科学基金(2011GXNSFA018136)

摘　　要：为研究一类具有时滞和HollingⅡ类功能反应捕食者-食饵模型,由于该模型的捕食者和食饵都具有密度制约,引入时滞对模型加以讨论,通过分析特征方程和构造适当的Lyapunov泛函,得到正平衡点存在及全局稳定的充分条件。研究结果表明,时滞对系统的稳定性起了重要作用,并为生物资源管理提供了策略。A predator-prey system with Holling functional response and time-delays is investigated.Both prey and predator are densite-dependent and the time delay is also been taken into consideration.By analyzing the corresponding characteristic and constructing a suitable Lyapunov functional,the existence of the equilibrium points is proved,and the sufficient conditions are derived for the global asymptotic stability of the positive equilibrium.The existence of Hopf bifurcation is also discussed.The results show that the time-delay plays an important role for the stability of the system,and provides tactics for the biological resource management.

关 键 词：时滞 稳定性 功能反应 HOPF分支 LYAPUNOV泛函 

分 类 号：O175.13[理学—数学]