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Approximation behavior of Van der Pol equation: Large and small nonlinearity parameter

Azarkhalili, B ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. Publisher: 2011
  3. Abstract:
  4. The labels mathematician, engineer, and physicist have all been used in reference to Balthazar van der Pol. The van der Pol oscillator, which we study in this paper, is a model developed by him to describe the behavior of nonlinear vacuum tube circuits in the relatively early days of the development of electronics technology. Our study in this paper will be based entirely on numerical solutions. The rigorous foundations for the analysis (e.g., the proof that the equation has a limit cycle solution which is a global attractor) date back to the work of Lienard in 1928, with later more general analysis by Levinson and others
  5. Keywords:
  6. Lienard theorem ; Limit cycle ; Regular perturbation ; Two-timing ; Van der Pol equation ; Circuit oscillations ; Computer science ; Engineers ; Control nonlinearities
  7. Source: IMECS 2011 - International MultiConference of Engineers and Computer Scientists 2011, 16 March 2011 through 18 March 2011 ; Volume 2 , March , 2011 , Pages 1539-1544 ; 9789881925121 (ISBN)
  8. URL: http://www.iaeng.org/publication/IMECS2011/IMECS2011_pp1539-1544.pdf