Abstract
The definition of a relaxation oscillation is presented. A review of the proofs of existence of periodic solutions of singularly perturbed systems is given. One such. a method, based upon the extension theorem, is worked out. The different asymptotic solutions of the Van der Pol oscillator are given in detail. A similar asymptotic analysis of the Volterra-Lotka equations is made. We deal with Van der Pol oscillators with a stochastic and a constant forcing term and finally construct a chaotic relaxation oscillator.
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© 1987 Springer Science+Business Media New York
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Grasman, J. (1987). Free Oscillation. In: Asymptotic Methods for Relaxation Oscillations and Applications. Applied Mathematical Sciences, vol 63. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1056-6_2
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DOI: https://doi.org/10.1007/978-1-4612-1056-6_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96513-0
Online ISBN: 978-1-4612-1056-6
eBook Packages: Springer Book Archive