• DOI:10.1063/1.3445770
• Corpus ID: 122648899

Series solutions of coupled Van der Pol equation by means of homotopy analysis method

@article{Li2010SeriesSO,
  title={Series solutions of coupled Van der Pol equation by means of homotopy analysis method},
  author={Yajie Li and Ben T. Nohara and Shijun Liao},
  journal={Journal of Mathematical Physics},
  year={2010},
  volume={51},
  pages={063517}
}

• Yajie Li, B. T. Nohara, S. Liao
• Published 28 June 2010
• Mathematics
• Journal of Mathematical Physics

In this paper, the homotopy analysis method (HAM) is used to give series solutions of self-exited oscillation systems governed by two Van der Pol equations, which are coupled by a linear and a cubic term. The frequency and amplitude of all possible periodic solutions are investigated. It is found that there exist either in-phase or out-of-phase periodic solutions only. Besides, the in-phase periodic oscillations are decoupled, whose periods and amplitudes have nothing to do with the linear and cubic coupled terms. However, the out-of-phase periodic oscillations are strongly coupled, whose period and amplitude can be controlled by the linear and cubic coupled terms.