The role of asymmetrical and repulsive coupling in the dynamics of two coupled van der Pol oscillators

Sergey Astakhov; Artem Gulai; Naoya Fujiwara; Jürgen Kurths

doi:10.1063/1.4940967

The role of asymmetrical and repulsive coupling in the dynamics of two coupled van der Pol oscillators

Sergey Astakhov, Artem Gulai, Naoya Fujiwara, Jürgen Kurths

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

A system of two asymmetrically coupled van der Pol oscillators has been studied. We show that the introduction of a small asymmetry in coupling leads to the appearance of a "wideband synchronization channel" in the bifurcational structure of the parameter space. An increase of asymmetry and transition to repulsive interaction leads to the formation of multistability. As the result, the tip of the Arnold's tongue widens due to the formation of folds defined by saddle-node bifurcation curves for the limit cycles on the torus.

Original language	English
Article number	023102
Journal	Chaos
Volume	26
Issue number	2
DOIs	https://doi.org/10.1063/1.4940967
Publication status	Published - 2016 Feb 1
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)
Applied Mathematics

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10.1063/1.4940967

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abstract = "A system of two asymmetrically coupled van der Pol oscillators has been studied. We show that the introduction of a small asymmetry in coupling leads to the appearance of a {"}wideband synchronization channel{"} in the bifurcational structure of the parameter space. An increase of asymmetry and transition to repulsive interaction leads to the formation of multistability. As the result, the tip of the Arnold's tongue widens due to the formation of folds defined by saddle-node bifurcation curves for the limit cycles on the torus.",

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AU - Astakhov, Sergey

AU - Gulai, Artem

AU - Fujiwara, Naoya

AU - Kurths, Jürgen

N1 - Funding Information: S.A. was supported by RFBR, Research Project No. 16-37-00104. N.F. was supported by CREST, JST. J.K. was supported by the IRTG 1740/TRP 2011/50151-0. Publisher Copyright: © 2016 AIP Publishing LLC.

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N2 - A system of two asymmetrically coupled van der Pol oscillators has been studied. We show that the introduction of a small asymmetry in coupling leads to the appearance of a "wideband synchronization channel" in the bifurcational structure of the parameter space. An increase of asymmetry and transition to repulsive interaction leads to the formation of multistability. As the result, the tip of the Arnold's tongue widens due to the formation of folds defined by saddle-node bifurcation curves for the limit cycles on the torus.

AB - A system of two asymmetrically coupled van der Pol oscillators has been studied. We show that the introduction of a small asymmetry in coupling leads to the appearance of a "wideband synchronization channel" in the bifurcational structure of the parameter space. An increase of asymmetry and transition to repulsive interaction leads to the formation of multistability. As the result, the tip of the Arnold's tongue widens due to the formation of folds defined by saddle-node bifurcation curves for the limit cycles on the torus.

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The role of asymmetrical and repulsive coupling in the dynamics of two coupled van der Pol oscillators

Abstract

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