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Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (8): 873-877.

• 论文 • 上一篇    下一篇

SOME DYNAMICAL BEHAVIOR OF THE STUART-LANDAU EQUATION WITH A PERIODIC EXCITATION

陈芳启1,4, 梁建术2, 陈予恕3   

  1. 1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China;
    2. College of Mechanical and Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang 050054, P. R. China;
    3. Department of Mechanics, Tianjin University, Tianjin 300072, P. R. China;
    4. Liu Hui Center for Applied Mathematics, Nankai University and Tianjin University, Tianjin 300072, P. R. China
  • 收稿日期:2003-01-16 修回日期:2004-03-09 出版日期:2004-08-18 发布日期:2004-08-18
  • 基金资助:
    the National Natural Science Foundation of China(10251001)

SOME DYNAMICAL BEHAVIOR OF THE STUART-LANDAU EQUATION WITH A PERIODIC EXCITATION

CHEN Fang-qi1,4, LIANG Jian-shu2, CHEN Yu-shu3   

  1. 1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China;
    2. College of Mechanical and Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang 050054, P. R. China;
    3. Department of Mechanics, Tianjin University, Tianjin 300072, P. R. China;
    4. Liu Hui Center for Applied Mathematics, Nankai University and Tianjin University, Tianjin 300072, P. R. China
  • Received:2003-01-16 Revised:2004-03-09 Online:2004-08-18 Published:2004-08-18
  • Supported by:
    the National Natural Science Foundation of China(10251001)

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摘要： 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 are 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.

关键词: Stuart-Landau equation, bifurcation, universal unfolding, germ

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 are 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

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