New approach to study the van der Pol equation for large damping
| dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
| dc.bibliographicCitation.volume | 2422 | |
| dc.contributor.author | Schneider, Klaus R. | |
| dc.date.accessioned | 2017-09-28T00:59:26Z | |
| dc.date.available | 2019-06-28T08:02:57Z | |
| dc.date.issued | 2017 | |
| dc.description.abstract | We present a new approach to establish the existence of a unique limit cycle for the van der Pol equation in case of large damping. It is connected with the bifurcation of a stable hyperbolic limit cycle from a closed curve composed of two heteroclinic orbits and of two segments of a straight line forming continua of equilibria. The proof is based on a linear time scaling (instead of the nonlinear Liénard transformation in previous approaches), on a Dulac-Cherkas function and the property of rotating vector fields. | eng |
| dc.description.version | publishedVersion | eng |
| dc.format | application/pdf | |
| dc.identifier.issn | 2198-5855 | |
| dc.identifier.uri | https://doi.org/10.34657/2732 | |
| dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/1948 | |
| dc.language.iso | eng | eng |
| dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
| dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2422 | |
| dc.relation.issn | 0946-8633 | eng |
| dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
| dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
| dc.subject.ddc | 510 | eng |
| dc.subject.other | Relaxation oscillation | eng |
| dc.subject.other | Dulac-Cherkas function | eng |
| dc.subject.other | rotated vector field | eng |
| dc.title | New approach to study the van der Pol equation for large damping | eng |
| dc.type | Report | eng |
| dc.type | Text | eng |
| tib.accessRights | openAccess | eng |
| wgl.contributor | WIAS | eng |
| wgl.subject | Mathematik | eng |
| wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |