Modal synchronization of coupled bistable van der Pol oscillators

I. B. Shiroky; Oleg Gendelman

doi:10.1016/j.chaos.2020.110555

Modal synchronization of coupled bistable van der Pol oscillators

I. B. Shiroky, Oleg Gendelman

Technion - Israel Institute of Technology

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

Abstract

The paper revisits recently revealed regimes of “nonconventional synchronization” in systems of coupled bi-stable van der Pol oscillators. These regimes are characterized by periodic (or quasiperiodic) almost complete energy exchanges between the coupled oscillators. In the paper it is demonstrated that such responses correspond to synchronization of the modulation amplitudes between symmetric and antisymmetric modes of the system, with persistent phase drift. This observation substantially simplifies the treatment, reduces the dynamics to a simple phase cylinder and allows to reveal a rich set of global and local bifurcations of limit cycles and tori in the system. Among other findings, one encounters an unexpected regime of nonstationary asymmetric synchronization.

Original language	English
Article number	110555
Journal	Chaos, Solitons and Fractals
Volume	143
DOIs	https://doi.org/10.1016/j.chaos.2020.110555
State	Published - Feb 2021

Keywords

Coupled oscillators
Global bifurcation
Limit cycle
Modal space
Synchronization

All Science Journal Classification (ASJC) codes

Applied Mathematics
Statistical and Nonlinear Physics
General Physics and Astronomy
General Mathematics

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10.1016/j.chaos.2020.110555

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title = "Modal synchronization of coupled bistable van der Pol oscillators",

abstract = "The paper revisits recently revealed regimes of “nonconventional synchronization” in systems of coupled bi-stable van der Pol oscillators. These regimes are characterized by periodic (or quasiperiodic) almost complete energy exchanges between the coupled oscillators. In the paper it is demonstrated that such responses correspond to synchronization of the modulation amplitudes between symmetric and antisymmetric modes of the system, with persistent phase drift. This observation substantially simplifies the treatment, reduces the dynamics to a simple phase cylinder and allows to reveal a rich set of global and local bifurcations of limit cycles and tori in the system. Among other findings, one encounters an unexpected regime of nonstationary asymmetric synchronization.",

keywords = "Coupled oscillators, Global bifurcation, Limit cycle, Modal space, Synchronization",

author = "Shiroky, {I. B.} and Oleg Gendelman",

note = "Funding Information: The authors are very grateful to Israel Science Foundation (grant 1697/17 ) for financial support.",

year = "2021",

month = feb,

doi = "10.1016/j.chaos.2020.110555",

language = "الإنجليزيّة",

volume = "143",

journal = "Chaos, Solitons and Fractals",

issn = "0960-0779",

publisher = "Elsevier Ltd.",

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TY - JOUR

T1 - Modal synchronization of coupled bistable van der Pol oscillators

AU - Shiroky, I. B.

AU - Gendelman, Oleg

N1 - Funding Information: The authors are very grateful to Israel Science Foundation (grant 1697/17 ) for financial support.

PY - 2021/2

Y1 - 2021/2

N2 - The paper revisits recently revealed regimes of “nonconventional synchronization” in systems of coupled bi-stable van der Pol oscillators. These regimes are characterized by periodic (or quasiperiodic) almost complete energy exchanges between the coupled oscillators. In the paper it is demonstrated that such responses correspond to synchronization of the modulation amplitudes between symmetric and antisymmetric modes of the system, with persistent phase drift. This observation substantially simplifies the treatment, reduces the dynamics to a simple phase cylinder and allows to reveal a rich set of global and local bifurcations of limit cycles and tori in the system. Among other findings, one encounters an unexpected regime of nonstationary asymmetric synchronization.

AB - The paper revisits recently revealed regimes of “nonconventional synchronization” in systems of coupled bi-stable van der Pol oscillators. These regimes are characterized by periodic (or quasiperiodic) almost complete energy exchanges between the coupled oscillators. In the paper it is demonstrated that such responses correspond to synchronization of the modulation amplitudes between symmetric and antisymmetric modes of the system, with persistent phase drift. This observation substantially simplifies the treatment, reduces the dynamics to a simple phase cylinder and allows to reveal a rich set of global and local bifurcations of limit cycles and tori in the system. Among other findings, one encounters an unexpected regime of nonstationary asymmetric synchronization.

KW - Coupled oscillators

KW - Global bifurcation

KW - Limit cycle

KW - Modal space

KW - Synchronization

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U2 - 10.1016/j.chaos.2020.110555

DO - 10.1016/j.chaos.2020.110555

M3 - مقالة

SN - 0960-0779

VL - 143

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

M1 - 110555

ER -

Modal synchronization of coupled bistable van der Pol oscillators

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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