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A homotopy analysis method for limit cycle of the van der Pol oscillator with delayed amplitude limiting

Eigoli, A. K ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1016/j.amc.2011.04.029
  3. Publisher: 2011
  4. Abstract:
  5. In this work, a powerful analytical method, called Liao's homotopy analysis method is used to study the limit cycle of a two-dimensional nonlinear dynamical system, namely the van der Pol oscillator with delayed amplitude limiting. It is shown that the solutions are valid for a wide range of variation of the system parameters. Comparison of the obtained solutions with those achieved by numerical solutions and by other perturbation techniques shows that the utilized method is effective and convenient to solve this type of problems with the desired order of approximation
  6. Keywords:
  7. Limit cycle ; van der Pol oscillator ; Analytical method ; Delayed amplitude limiting ; Homotopy analysis method ; Numerical solution ; Circuit oscillations ; Dynamical systems ; Lyapunov methods ; Nonlinear dynamical systems ; Numerical methods ; Oscillators (mechanical) ; Perturbation techniques
  8. Source: Applied Mathematics and Computation ; Volume 217, Issue 22 , July , 2011 , Pages 9404-9411 ; 00963003 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0096300311005868