AAM  >> Vol. 3 No. 4 (November 2014)

    一类具有迁移率和Holling-II型功能性反应的时滞捕食–食饵模型
    A Delayed Predator-Prey Model with Migration Rate and Holling-II Type Functional Response

  • 全文下载: PDF(823KB) HTML    PP.231-244   DOI: 10.12677/AAM.2014.34033  
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作者:  

段全恒,郭志明:广州大学数学与信息科学学院,广州

关键词:
时滞微分方程系统Holling-II型功能性反应迁移率稳定性Hopf分支Delayed Differential System Holling-II Functional Response Migration Rate Stability Hopf Bifurcation

摘要:

本文研究了一类捕食者具有人工控制迁移率的Holling-II型功能性反应的捕食-食饵模型的全局动力学性质。由于捕食者的捕食行为对其数量的变化有滞后效应,所以该模型是一个时滞微分方程组。首先研究了该系统平衡点的存在性和稳定性;接着以时滞为参数,分析Hopf分支存在的充分条件;利用中心流形定理和正规型理论给出确定Hopf分支周期解方向和稳定性的计算公式;最后对于理论结果给出了相应的数值模拟。

In this paper, we study global dynamic properties of a predator-prey model with Holling-II func- tional response and predator migration, which reflect manual control. Because of the delay effect of predations on the variation of predator’s quantity, this model is a system of delayed differential equations. Firstly, we study the existence and stability of equilibria. Then, sufficient conditions are obtained which ensures that Hopf bifurcation occurs when the delay is regarded as a bifurcation parameter. We also derive computational formula for direction and stability of Hopf bifurcation by applying the center manifold theorem and norm form theory. Some numerical simulations illu-strate the theoretical results.

文章引用:
段全恒, 郭志明. 一类具有迁移率和Holling-II型功能性反应的时滞捕食–食饵模型[J]. 应用数学进展, 2014, 3(4): 231-244. http://dx.doi.org/10.12677/AAM.2014.34033

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