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

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Authors

ŠEVČÍK Jan PŘIBYLOVÁ Lenka

Year of publication 2022
Type Article in Proceedings
Conference The 14th CHAOS 2021 International Conference
MU Faculty or unit

Faculty of Science

Citation
Web https://link.springer.com/chapter/10.1007/978-3-030-96964-6_29
Doi http://dx.doi.org/10.1007/978-3-030-96964-6_29
Keywords Synchronization; Van der Pol oscillator; Bifurcations of limit cycles; Neimark–Sacker bifurcation; q-fold bifurcation; Arnold tongues
Description 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.
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