Forced van der Pol Oscillator—Synchronization from the
Bifurcation Theory Point of View

D 2022

Forced van der Pol Oscillator—Synchronization from the Bifurcation Theory Point of View

ŠEVČÍK, Jan and Lenka PŘIBYLOVÁ

Basic information

Original name

Forced van der Pol Oscillator—Synchronization from the Bifurcation Theory Point of View

Authors

ŠEVČÍK, Jan (203 Czech Republic, belonging to the institution) and Lenka PŘIBYLOVÁ (203 Czech Republic, guarantor, belonging to the institution)

Edition

Cham, The 14th CHAOS 2021 International Conference, p. 411-420, 10 pp. 2022

Publisher

Springer

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10102 Applied mathematics

Country of publisher

Switzerland

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

printed version "print"

References:

URL

RIV identification code

RIV/00216224:14310/22:00126265

Organization unit

Faculty of Science

ISBN

978-3-030-96963-9

ISSN

DOI

http://dx.doi.org/10.1007/978-3-030-96964-6_29

Keywords in English

Synchronization; Van der Pol oscillator; Bifurcations of limit cycles; Neimark–Sacker bifurcation; q-fold bifurcation; Arnold tongues

Abstract

V originále

The contribution presents a bifurcation theory point of view to synchronization of a forced van der Pol oscillator, which is coupled to a master oscillator as a system with a stable limit cycle corresponding to harmonic oscillation. We present bifurcation manifolds, 3D sections of the phase space and its Poincaré sections for parameters close to these manifolds providing a clear visualization of the dynamics of the 4D system. Among other things, we present the coexistence of a stable torus and a stable cycle arising from q-fold bifurcation on an Arnold tongue.

Links

MUNI/A/1615/2020, interní kód MU

Name: Matematické a statistické modelování 5 (Acronym: MaStaMo5)

Investor: Masaryk University

Citovat

ŠEVČÍK, Jan and Lenka PŘIBYLOVÁ. Forced van der Pol Oscillator—Synchronization from the Bifurcation Theory Point of View. In Skiadas, C.H., Dimotikalis, Y. The 14th CHAOS 2021 International Conference. Cham: Springer, 2022, p. 411-420. ISBN 978-3-030-96963-9. Available from: https://dx.doi.org/10.1007/978-3-030-96964-6_29.

@inproceedings{1874691,
   author = {Ševčík, Jan and Přibylová, Lenka},
   address = {Cham},
   booktitle = {The 14th CHAOS 2021 International Conference},
   doi = {http://dx.doi.org/10.1007/978-3-030-96964-6_29},
   editor = {Skiadas, C.H., Dimotikalis, Y.},
   keywords = {Synchronization; Van der Pol oscillator; Bifurcations of limit cycles; Neimark–Sacker bifurcation; q-fold bifurcation; Arnold tongues},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Cham},
   isbn = {978-3-030-96963-9},
   pages = {411-420},
   publisher = {Springer},
   title = {Forced van der Pol Oscillator—Synchronization from the Bifurcation Theory Point of View},
   url = {https://link.springer.com/chapter/10.1007/978-3-030-96964-6_29},
   year = {2022}
}

TY  - JOUR
ID  - 1874691
AU  - Ševčík, Jan - Přibylová, Lenka
PY  - 2022
TI  - Forced van der Pol Oscillator—Synchronization from the Bifurcation Theory Point of View
PB  - Springer
CY  - Cham
SN  - 9783030969639
KW  - Synchronization
KW  - Van der Pol oscillator
KW  - Bifurcations of limit cycles
KW  - Neimark–Sacker bifurcation
KW  - q-fold bifurcation
KW  - Arnold tongues
UR  - https://link.springer.com/chapter/10.1007/978-3-030-96964-6_29
N2  - The contribution presents a bifurcation theory point of view to synchronization of a forced van der Pol oscillator, which is coupled to a master oscillator as a system with a stable limit cycle corresponding to harmonic oscillation. We present bifurcation manifolds, 3D sections of the phase space and its Poincaré sections for parameters close to these manifolds providing a clear visualization of the dynamics of the 4D system. Among other things, we present the coexistence of a stable torus and a stable cycle arising from q-fold bifurcation on an Arnold tongue.
ER  -

ŠEVČÍK, Jan and Lenka PŘIBYLOVÁ. Forced van der Pol Oscillator—Synchronization from the Bifurcation Theory Point of View. In Skiadas, C.H., Dimotikalis, Y. \textit{The 14th CHAOS 2021 International Conference}. Cham: Springer, 2022, p.~411-420. ISBN~978-3-030-96963-9. Available from: https://dx.doi.org/10.1007/978-3-030-96964-6\_{}29.

Detailed Information on Publication Record