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Analytical solution for Van der Pol–Duffing oscillators

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  • Kimiaeifar, A.
  • Saidi, A.R.
  • Bagheri, G.H.
  • Rahimpour, M.
  • Domairry, D.G.

Abstract

In this paper, the problem of single-well, double-well and double-hump Van der Pol–Duffing oscillator is studied. Governing equation is solved analytically using a new kind of analytic technique for nonlinear problems namely the “Homotopy Analysis Method” (HAM), for the first time. Present solution gives an expression which can be used in wide range of time for all domain of response. Comparisons of the obtained solutions with numerical results show that this method is effective and convenient for solving this problem. This method is a capable tool for solving this kind of nonlinear problems.

Suggested Citation

  • Kimiaeifar, A. & Saidi, A.R. & Bagheri, G.H. & Rahimpour, M. & Domairry, D.G., 2009. "Analytical solution for Van der Pol–Duffing oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2660-2666.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:2660-2666
    DOI: 10.1016/j.chaos.2009.03.145
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    References listed on IDEAS

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    1. Njah, A.N. & Vincent, U.E., 2008. "Chaos synchronization between single and double wells Duffing–Van der Pol oscillators using active control," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1356-1361.
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    Cited by:

    1. Beregov, R.Y. & Melkikh, A.V., 2015. "De-synchronization and chaos in two inductively coupled Van der Pol auto-generators," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 17-28.
    2. Youhua Qian & Shuli Wang & Shuping Chen, 2023. "Multi-Frequency Homotopy Analysis Method for Coupled Van der Pol-Duffing System with Time Delay," Mathematics, MDPI, vol. 11(2), pages 1-17, January.

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