| Brusselator系统的Hopf分岔 |
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| 引用本文： | 于晋臣,李树彬.Brusselator系统的Hopf分岔[J].山东科学,2007,20(1):19-24,29. |
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| 作者姓名： | 于晋臣 李树彬 |
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| 作者单位： | 北京交通大学理学院,北京,100044;山东省科学院自动化研究所,山东,济南,250014 |
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| 摘 要： | 本文主要研究Brusselator系统的动力行为.首先,分析了系统产生Hopf分岔的原因,然后详细讨论了Brusselator系统平衡点的稳定性,并且证明了Brusselator系统当临界平衡点失稳时会产生超临界Hopf分岔,即从平衡点处分岔出稳定的极限环,进而得到了Brusselator系统出现Hopf分岔所需的参数条件;最后,数值模拟的结果显示了与理论分析的一致性.
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| 关 键 词： | Hopf分岔 平衡点 稳定性 特征值 |
| 文章编号： | 1002-4026（2007）01-0019-06 |
| 收稿时间： | 2006-04-20 |
| 修稿时间： | 2006-04-20 |
Hopf Bifurcation in Brusselator System |
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| YU Jin-chen,LI Shu-bin.Hopf Bifurcation in Brusselator System[J].Shandong Science,2007,20(1):19-24,29. |
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| Authors: | YU Jin-chen LI Shu-bin |
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| Institution: | 1. School of Sciences, Beijing Jiaotong University, Beijing 100044, China ; 2. Institute of Automation, S handottg Aeademy of Sciences , Jinan 250014, China |
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| Abstract: | The dynamical behavior of Brusselator system was considered.The mathematical mechanism of Hopf(bifurcation) was analyzed,and the stability of equilibrium was disscussed in detail.When the critical equilibrium loses its stability,supercritical Hopf bifurcation occurs.Hence,a stable periodic orbit bifrcates from the critical equilibrium.At the same time,the condition of parameter to ensure the appear of Hopf(bifurcation) in Brusselator system was obtained.The result of numerical simulatior correspondented with that of theoretical analysis. |
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| Keywords: | Hopf bifurcation equilibrium stability eigenvalue |
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