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一类具时滞和阶段结构的捕食模型的稳定性与Hopf分支 被引量：6

Hopf bifurcation of a stage-structured predator-prey model with time delay
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摘要 研究一类具有时滞和阶段结构的捕食模型的稳定性和Hopf分支的存在性问题.通过分析特征方程,得到了正平衡点局部稳定的条件.同时,应用中心流形定理和规范型理论,得到了确定Hopf分支方向和分支周期解的稳定性的计算公式.最后对所得理论结果进行了数值模拟. A stage-structured predator-prey model with time delay and Holling type Ⅲ functional response is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated. The existence of Hopf bifurcations is established. Formulas are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results.
作者 田晓红 徐瑞
机构地区 军械工程学院应用数学研究所
出处 《高校应用数学学报（A辑）》 CSCD 北大核心 2010年第3期285-292,共8页 Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金 国家自然科学基金(10671209)
关键词 捕食系统 时滞 功能性反应 HOPF分支 稳定性 predator-prey system time delay functional response Hopf bifurcation stability
分类号 O175.1 [理学—基础数学]
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参考文献8

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二级参考文献15

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共引文献30

同被引文献31

  • 1徐瑞,郝飞龙,陈兰荪.一个具有时滞和阶段结构的捕食-被捕食模型[J].数学物理学报（A辑）,2006,26(3):387-395. 被引量：30
  • 2邓祥周,田立新,段希波.能源价格的动态模型及分析[J].统计与决策,2007,23(2):9-10. 被引量：15
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  • 8Xiao Yan Ni, Chen Lan Sun. Global stability of a predator-prey system with stage structure for the predator[J]. Acta Mathematica Sinica, English Series, 2003, 19(2):1-11.
  • 9Song Xin Yu, Cai Li Ming, Neumann A U. Ratio-dependent predator-prey system with stage structure for prey[J]. Discrete and Continuous Dynamical System-Series B, 2004, 3(4):747-758.
  • 10Kar T K, Pahari U K. Modeling and analysis of a prey-predator system with stage-structure and harvest- ing[J]. Nonlinear Analysis, 2007, 2(8):601-609.

引证文献6

二级引证文献10

高校应用数学学报（A辑）
2010年 第3期

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