| 双时滞物价瑞利方程的Hopf型和余维2型分支分析 |
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| 引用本文： | 吕堂红,周林华. 双时滞物价瑞利方程的Hopf型和余维2型分支分析[J]. 吉林大学学报(理学版), 2012, 50(3): 409-416 |
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| 作者姓名： | 吕堂红 周林华 |
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| 作者单位： | 长春理工大学 理学院, 长春 130022 |
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| 摘 要： | 研究具有两个离散时滞的物价瑞利模型的动力学性质. 用线性稳定性方法和Nyquist准则, 讨论了系统平衡点的局部稳定性和Hopf分支的存在性; 用规范型理论和中心流形定理给出了确定分支方向及分支周期解稳定性的计算公式; 证明了模型中可以出现余维2分支, 并给出了在a-τ参数平面内平衡点的局部稳定区域图. 数值模拟验证了理论分析结果.
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| 关 键 词： | 物价瑞利方程； 双时滞； Hopf分支； 余维2分支； 分支方向； 稳定性； 周期解 |
| 收稿时间： | 2011-08-22 |
Hopf and Codimension Two Bifurcation in Price Rayleigh Equation with Two Time Delays |
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| Lü Tang-hong , ZHOU Lin-hua. Hopf and Codimension Two Bifurcation in Price Rayleigh Equation with Two Time Delays[J]. Journal of Jilin University: Sci Ed, 2012, 50(3): 409-416 |
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| Authors: | Lü Tang-hong ZHOU Lin-hua |
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| Affiliation: | College of Science, Changchun University of Science and Technology, Changchun 130022, China |
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| Abstract: | The authors studied dynamics of the Rayleigh model with two discrete time-delays of the price.First using the linear stability method and the Nyquist criterion,we discussed the local stability of the system equilibrium point and the existence of Hopf bifurcation,then used normal form and the center manifold theorem to determine the formula of the branch direction and branch stability of periodic solutions.In addition,in the model codimension 2 branch can appear,and we gave the local area map of the parameter a-τ plane stable equilibrium point,finally,via numerical simulation we verified the theoretical analysis. |
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| Keywords: | price Rayleigh equation two delay Hopf bifurcation codimension two bifurcation direction of bifurcation stability periodic solution |
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