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

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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

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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