Abstract
In this work it is shown that by a series of transformations the classical Van der Pol oscillator can be exactly reduced to Abel's equations of the second kind. The absence of exact analytic solutions in terms of known (tabulated) functions of the reduced equations leads to the conclusion that there are no exact solutions of the Van der Pol oscillator in terms of known (tabulated) functions. In the limits or small or large values of the parameter e the reduced equations are amenable to asymptotic analysis. For the case of large values of the parameter (relaxation oscillations) an analytic solution to the problem is provided that is exact up to O(ε -2).
Original language | English (US) |
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Pages (from-to) | 611-615 |
Number of pages | 5 |
Journal | ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik |
Volume | 83 |
Issue number | 9 |
DOIs | |
State | Published - 2003 |
Keywords
- Asymptotic solutions
- Van der Pol oscillator
ASJC Scopus subject areas
- Computational Mechanics
- Applied Mathematics