| Lotka-Volterra捕食方程的Hopf分岔研究 |
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| 引用本文： | 张洁,田艳芳,汪益川. Lotka-Volterra捕食方程的Hopf分岔研究[J]. 后勤工程学院学报, 2012, 0(3): 87-91 |
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| 作者姓名： | 张洁 田艳芳 汪益川 |
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| 作者单位： | 后勤工程学院基础部;后勤工程学院科研部 |
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| 摘 要： | 对于具有有限时滞的Lotka-Volterra捕食方程,选用时滞作为分岔参数,得到模型的局部稳定性条件和系统的Hopf分岔值。利用中心流行定理和正则化方法,得到Hopf分岔的方向和周期解的稳定性。
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| 关 键 词： | Lotka-Volterra方程 时滞 稳定性 Hopf分岔 周期解 |
Stability and Hopf Bifurcation Analysis for Lotka-Volterra Equation with Time Delay |
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| ZHANG Jie,TIAN Yan-fang,WANG Yi-chuan. Stability and Hopf Bifurcation Analysis for Lotka-Volterra Equation with Time Delay[J]. Journal of Logistical Engineering University, 2012, 0(3): 87-91 |
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| Authors: | ZHANG Jie TIAN Yan-fang WANG Yi-chuan |
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| Affiliation: | 1.Dept.of Foundation Studies,LEU,Chongqing 401311,China; 2.Dept.of Science & Research,LEU,Chongqing 401311,China) |
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| Abstract: | Time delay as the bifurcation parameter is adopted to study Lotka-Volterra equation model with finite time delay,deriving the local stability of this model by analyzing the associated transcendental equation and the direction of Hopf bifurcation as well as the stability of periodic solution.The results show that the Hopf bifurcation occurs when the delay passes a sequence of critical values.The stability and the direction of the Hopf bifurcation are determined by applying the normal form approach and the center manifold theory.Finally,numerical simulation is given to verify the results. |
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| Keywords: | Lotka-Volterra equation time delay stability Hopf bifurcation periodic solution |
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