Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (1): 68-75.

• 论文 • 上一篇    下一篇

STRONGLY RESONANT BIFURCATIONS OF NONLINEARLY COUPLED VAN DER POL-DUFFING OSCILLATOR

甘春标, 陆启韶, 黄克累   

  1. Department of Applied Mathematics and Physics, Peking University of Aeronautics and Astronautics, Beijing 100083, P. R. China
  • 收稿日期:1997-03-26 出版日期:1999-01-18 发布日期:1999-01-18
  • 基金资助:

    This work was partially supported by the National Natural Science Foundation of China, the Science Foundation of Aviation of China and the Doctoral Education Foundation of China

STRONGLY RESONANT BIFURCATIONS OF NONLINEARLY COUPLED VAN DER POL-DUFFING OSCILLATOR

Gan Chunbiao, Lu Qishao, Huang Kelei   

  1. Department of Applied Mathematics and Physics, Peking University of Aeronautics and Astronautics, Beijing 100083, P. R. China
  • Received:1997-03-26 Online:1999-01-18 Published:1999-01-18
  • Supported by:

    This work was partially supported by the National Natural Science Foundation of China, the Science Foundation of Aviation of China and the Doctoral Education Foundation of China

摘要: In this paper, the strongly resonant bifurcations of a nonlinearly coupled Van der Pol-Duffing Oscillator by the classical multi-scale method are studied. It is shown that there exist Periodic motions of a single oscillator, frequency-locking andquasi-periodic motions of two oscillators when the parameters vary. Meanwhile,some numerical results are given to test the theoretical ones.

关键词: nonlinearly coupling, multi-scale method, frequency-locking, Quasiperiodic

Abstract: In this paper, the strongly resonant bifurcations of a nonlinearly coupled Van der Pol-Duffing Oscillator by the classical multi-scale method are studied. It is shown that there exist Periodic motions of a single oscillator, frequency-locking andquasi-periodic motions of two oscillators when the parameters vary. Meanwhile,some numerical results are given to test the theoretical ones.

Key words: nonlinearly coupling, multi-scale method, frequency-locking, Quasiperiodic

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