Asymptotic Methods for Relaxation Oscillations and Applications (Applied Mathematical Sciences) by Johan Grasman
Asymptotic Methods for Relaxation Oscillations and Applications (Applied Mathematical Sciences) (Volume 63) by Johan Grasman
English | Apr 3, 1987 | ISBN: 0387965130, 3540965130 | 235 Pages | DJVU | 2 MB
English | Apr 3, 1987 | ISBN: 0387965130, 3540965130 | 235 Pages | DJVU | 2 MB
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.