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Strongly resonant bifurcations of nonlinearly coupled van der Pol-Duffing Oscillator

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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 and quasi-periodic motions of two oscillators when the parameters vary. Meanwhile, some numerical results are given to test the theoretical ones.

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Authors and Affiliations

  1. Department of Applied Mathematics and Physics, Peking University of Aeronautics and Astronautics, 100083, Beijing, P. R. China

    Gan Chunbiao, Lu Qishao & Huang Kelei

Authors
  1. Gan Chunbiao
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  2. Lu Qishao
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  3. Huang Kelei
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Additional information

Communicated by Li Li

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

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Chunbiao, G., Qishao, L. & Kelei, H. Strongly resonant bifurcations of nonlinearly coupled van der Pol-Duffing Oscillator. Appl Math Mech 20, 68–75 (1999). https://doi.org/10.1007/BF02459275

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  • DOI: https://doi.org/10.1007/BF02459275

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