Some Dynamical Behavior of the Stuart-Landau Equation With a Periodic Excitation
-
摘要: 研究了周期激励Stuart-Landau方程的锁频周期解.利用奇异性理论分别研究了这些解关于外部激励振幅和频率的分岔行为.结果表明:关于外部激励振幅的普适开折具有余维3,在某些条件下,得到了转迁集及分岔图.另外还证明:关于频率的分岔问题具有无穷余维,因此该情形下的动力学分岔行为非常复杂.发现了一些新的动力学现象,它们是孙亮等所获结果的补充.
-
关键词:
- Stuart-Landau方程 /
- 分岔 /
- 普适开折 /
- 芽
Abstract: The lock-in periodic solutions of the Stuart-Landau equation with a periodic excitation are studied. Using singularity theory, the bifurcation behavior of these solutions with respect to the excitation amplitude and frequency were investigated in detail, respectively. The results show that the universal unfolding with respect to the excitation amplitude possesses codimension 3. The transition sets in unfolding parameter plane and the bifurcation diagrams are plotted under some conditions. Additionally, it has also been proved that the bifurcation problem with respect to frequence possesses infinite codimension. Therefore the dynamical bifurcation behavior is very complex in this case. Some new dynamical phenomena are presented, which are the supplement of the results obtained by Sun Liang et al.-
Key words:
- Stuart-Landau equation /
- bifurcation /
- universal unfolding /
- germ
-
[1] 孙亮,胡国辉,孙德军,等.激励 Stuart-Landau方程的研究:周期解、稳定性及流动控制[J].力学学报,2002,34(4):519—527. [2] Provansal M, Mathis C, Boyer L. Benard-von Krmn instability: transient and forced regimes[J].J Fluid Mech,1987,182:1—22. doi: 10.1017/S0022112087002222 [3] Golubitsky M, Schaeffer D G.Singularities and Groups in Bifurcation Theory.Vol 1[M].New York: Springer-Verlag,1985. [4] 吴志强,陈予恕.具有单边约束的基本分岔问题的新分岔模式[J].应用数学和力学,2001,22(11):1135—1145. [5] CHEN Yu-shu, Langford W F. The subharmonic bifurcation solutions of nonlinear Mathieu equation and Euler dynamic buckling problems[J].Acta Mech Sinica,1988,4(4):350—362. doi: 10.1007/BF02486668 [6] CHEN Yu-shu, Andrew Y T L.Bifurcation and Chaos in Engineering[M].London:Springer-Verlag, 1998.
计量
- 文章访问数: 3163
- HTML全文浏览量: 171
- PDF下载量: 544
- 被引次数: 0