一类具有时滞的捕食者-食饵模型的稳定性和Hopf分支
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引用本文:张 婧,张 睿,周 震.一类具有时滞的捕食者-食饵模型的稳定性和Hopf分支[J].经济数学,2019,(2):23-27
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作者单位
张 婧,张 睿,周 震 (兰州交通大学 数理学院甘肃 兰州 730070) 
中文摘要:针对种群的发展趋势不仅依赖于当前的状态, 而且还依赖于过去某一时间段的状态.研究了一类带时滞的捕食者-食饵模型. 首先应用线性化方法分析该模型正平衡点的局部渐近稳定性, 然后以时滞为分支参数讨论Hopf分支的存在性, 最后对模型进行数值模拟证实了以上相关结果.
中文关键词:常微分方程  稳定性  线性化  时滞
 
Stability and Hopf Bifurcation for a Predator-Prey Model with Time Delay
Abstract:The development trend of a population depends not only on the current, but also on the state in a certain period of time in the past, a predator-prey model with time delay is investigated. First, the local asymptotic stability of the positive equilibrium is demonstrated by using linearization. Then, the existence of Hopf bifurcation is considered by choosing the time delay as the parameter. Finally, some numerical simulations are carried out to illustrate above results.
keywords:ordinary differential equation  stability  linearization  time delay
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