Asymptotic Methods for Relaxation Oscillations and Applications (Applied Mathematical Sciences, 63, Band 63) - Softcover

Grasman, Johan

Softcover

ISBN 10: 0387965130 ISBN 13: 9780387965130

Verlag: Springer, 2013

Inhaltsangabe

In various fields of science, notably in physics and biology, one is con­ fronted with periodic phenomena having a remarkable temporal structure: it is as if certain systems are periodically reset in an initial state. A paper of Van der Pol in the Philosophical Magazine of 1926 started up the investigation of this highly nonlinear type of oscillation for which Van der Pol coined the name "relaxation oscillation". The study of relaxation oscillations requires a mathematical analysis which differs strongly from the well-known theory of almost linear oscillations. In this monograph the method of matched asymptotic expansions is employed to approximate the periodic orbit of a relaxation oscillator. As an introduction, in chapter 2 the asymptotic analysis of Van der Pol's equation is carried out in all detail. The problem exhibits all features characteristic for a relaxation oscillation. From this case study one may learn how to handle other or more generally formulated relaxation oscillations. In the survey special attention is given to biological and chemical relaxation oscillators. In chapter 2 a general definition of a relaxation oscillation is formulated.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2013
• Sprache: Englisch
• ISBN 10: 0387965130
• ISBN 13: 9780387965130
• Einband: Taschenbuch
• Anzahl der Seiten: 240
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