Asymptotic Methods for Relaxation Oscillations and Applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1987
|
| Series: | Applied Mathematical Sciences
63 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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 |
| Physical Description: | 1 Online-Ressource (XIII, 227p. 85 illus) |
| ISBN: | 9781461210566 9780387965130 |
| ISSN: | 0066-5452 |
| DOI: | 10.1007/978-1-4612-1056-6 |
Staff View
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| isbn | 9781461210566 9780387965130 |
| issn | 0066-5452 |
| language | English |
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| spelling | Grasman, Johan 1944- Verfasser (DE-588)12056212X aut Asymptotic Methods for Relaxation Oscillations and Applications by Johan Grasman New York, NY Springer New York 1987 1 Online-Ressource (XIII, 227p. 85 illus) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 63 0066-5452 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 Physics Theoretical, Mathematical and Computational Physics Asymptotische Entwicklung (DE-588)4112609-9 gnd rswk-swf Ferroresonanzschwingung (DE-588)4138688-7 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Ferroresonanzschwingung (DE-588)4138688-7 s Asymptotik (DE-588)4126634-1 s 1\p DE-604 Asymptotische Entwicklung (DE-588)4112609-9 s 2\p DE-604 https://doi.org/10.1007/978-1-4612-1056-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Grasman, Johan 1944- Asymptotic Methods for Relaxation Oscillations and Applications Physics Theoretical, Mathematical and Computational Physics Asymptotische Entwicklung (DE-588)4112609-9 gnd Ferroresonanzschwingung (DE-588)4138688-7 gnd Asymptotik (DE-588)4126634-1 gnd |
| subject_GND | (DE-588)4112609-9 (DE-588)4138688-7 (DE-588)4126634-1 |
| title | Asymptotic Methods for Relaxation Oscillations and Applications |
| title_auth | Asymptotic Methods for Relaxation Oscillations and Applications |
| title_exact_search | Asymptotic Methods for Relaxation Oscillations and Applications |
| title_full | Asymptotic Methods for Relaxation Oscillations and Applications by Johan Grasman |
| title_fullStr | Asymptotic Methods for Relaxation Oscillations and Applications by Johan Grasman |
| title_full_unstemmed | Asymptotic Methods for Relaxation Oscillations and Applications by Johan Grasman |
| title_short | Asymptotic Methods for Relaxation Oscillations and Applications |
| title_sort | asymptotic methods for relaxation oscillations and applications |
| topic | Physics Theoretical, Mathematical and Computational Physics Asymptotische Entwicklung (DE-588)4112609-9 gnd Ferroresonanzschwingung (DE-588)4138688-7 gnd Asymptotik (DE-588)4126634-1 gnd |
| topic_facet | Physics Theoretical, Mathematical and Computational Physics Asymptotische Entwicklung Ferroresonanzschwingung Asymptotik |
| url | https://doi.org/10.1007/978-1-4612-1056-6 |
| work_keys_str_mv | AT grasmanjohan asymptoticmethodsforrelaxationoscillationsandapplications |