Yu. S. Ilyashenko, D. A. Ryzhov, D. A. Filimonov, “Phase-lock effect for equations modeling resistively shunted Josephson junctions and for their perturbations”, Funktsional. Anal. i Prilozhen., 45:3 (2011), 41–54; Funct. Anal. Appl., 45:3 (2011), 192

Funktsional'nyi Analiz i ego Prilozheniya

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Forthcoming papers
	Archive
	Impact factor
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Funktsional. Anal. i Prilozhen.:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Funktsional'nyi Analiz i ego Prilozheniya, 2011, Volume 45, Issue 3, Pages 41–54
DOI: https://doi.org/10.4213/faa3045 (Mi faa3045)

This article is cited in 24 scientific papers (total in 24 papers)

Phase-lock effect for equations modeling resistively shunted Josephson junctions and for their perturbations

Yu. S. Ilyashenko^abcd, D. A. Ryzhov^e, D. A. Filimonov^f

^a Moscow State University
^b Independent University of Moscow
^c Steklov Mathematical Institute
^d Cornell University, USA
^e Chebyshev Laboratory, Saint-Petersburg State University
^f 5.Moscow State University of Railway Engineering

Full-text PDF (237 kB) Citations (24)

References:

PDF

HTML

DOI: https://doi.org/10.4213/faa3045

Abstract: In this work we study dynamical systems on the torus modeling Josephson junctions in the theory of superconductivity, and also perturbations of these systems. We show that, in the family of equations that describe resistively shunted Josephson junctions, phase lock occurs only for integer rotation numbers and propose a simple method for calculating the boundaries of the corresponding Arnold tongues. This part is a simplification of known results about the quantization of rotation number [4]. Moreover, we show that the quantization of rotation number only at integer points is a phenomenon of infinite codimension. Namely, there is an infinite set of independent perturbations of systems that give rise to countably many nondiscretely located phase-locking regions.

Keywords: differential equations on the torus, perturbation theory, Josephson effect, phase lock, quantization of rotation number, Arnold tongues.

Received: 03.12.2010

English version:
Functional Analysis and Its Applications, 2011, Volume 45, Issue 3, Pages 192–203
DOI: https://doi.org/10.1007/s10688-011-0023-8

Bibliographic databases:

Document Type: Article

UDC: 517.923+517.925.54

Language: Russian

Citation: Yu. S. Ilyashenko, D. A. Ryzhov, D. A. Filimonov, “Phase-lock effect for equations modeling resistively shunted Josephson junctions and for their perturbations”, Funktsional. Anal. i Prilozhen., 45:3 (2011), 41–54; Funct. Anal. Appl., 45:3 (2011), 192–203

Citation in format AMSBIB

\Bibitem{IlyRyzFil11}

\by Yu.~S.~Ilyashenko, D.~A.~Ryzhov, D.~A.~Filimonov

\paper Phase-lock effect for equations modeling resistively shunted Josephson junctions and for their perturbations

\jour Funktsional. Anal. i Prilozhen.

\yr 2011

\vol 45

\issue 3

\pages 41--54

\mathnet{http://mi.mathnet.ru/faa3045}

\crossref{https://doi.org/10.4213/faa3045}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2883238}

\zmath{https://zbmath.org/?q=an:1271.34052}

\elib{https://elibrary.ru/item.asp?id=20730626}

\transl

\jour Funct. Anal. Appl.

\yr 2011

\vol 45

\issue 3

\pages 192--203

\crossref{https://doi.org/10.1007/s10688-011-0023-8}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000298226200004}

\elib{https://elibrary.ru/item.asp?id=18008005}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80053482678}

Linking options:

https://www.mathnet.ru/eng/faa3045

https://doi.org/10.4213/faa3045

https://www.mathnet.ru/eng/faa/v45/i3/p41

This publication is cited in the following 24 articles:

Alexey A. Glutsyuk, “Extended Model of Josephson Junction, Linear Systems with Polynomial Solutions, Determinantal Surfaces, and Painlevé III Equations”, Proc. Steklov Inst. Math., 326 (2024), 90–132
Alexey Glutsyuk, “On germs of constriction curves in model of overdamped Josephson junction, dynamical isomonodromic foliation and Painlevé 3 equation”, Mosc. Math. J., 23:4 (2023), 479–513
Y Bibilo, A A Glutsyuk, “On families of constrictions in model of overdamped Josephson junction and Painlevé 3 equation*”, Nonlinearity, 35:10 (2022), 5427
Julian M. I. Newman, Maxime Lucas, Aneta Stefanovska, Understanding Complex Systems, Physics of Biological Oscillators, 2021, 111
J. Newman, M. Lucas, A. Stefanovska, “Stabilization of cyclic processes by slowly varying forcing”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 31:12 (2021)
Glutsyuk A.A. Netay I.V., “On Spectral Curves and Complexified Boundaries of the Phase-Lock Areas in a Model of Josephson Junction”, J. Dyn. Control Syst., 26:4 (2020), 785–820
Chen Chris Gong, Ralf Toenjes, Arkady Pikovsky, “Coupled Möbius maps as a tool to model Kuramoto phase synchronization”, Phys. Rev. E, 102:2 (2020)
Ivan A Bizyaev, Ivan S Mamaev, “Dynamics of the nonholonomic Suslov problem under periodic control: unbounded speedup and strange attractors”, J. Phys. A: Math. Theor., 53:18 (2020), 185701
Borisov A. Mamaev I., “Rigid Body Dynamics”, Rigid Body Dynamics, de Gruyter Studies in Mathematical Physics, 52, Walter de Gruyter Gmbh, 2019, 1–520
S. I. Tertychnyi, “Solution space monodromy of a special double confluent Heun equation and its applications”, Theoret. and Math. Phys., 201:1 (2019), 1426–1441
A. A. Glutsyuk, “On Constrictions of Phase-Lock Areas in Model of Overdamped Josephson Effect and Transition Matrix of the Double-Confluent Heun Equation”, J Dyn Control Syst, 25:3 (2019), 323
Xu C., Boccaletti S., Guan Sh., Zheng Zh., “Origin of Bellerophon States in Globally Coupled Phase Oscillators”, Phys. Rev. E, 98:5 (2018), 050202
V. M. Buchstaber, A. A. Glutsyuk, “On monodromy eigenfunctions of Heun equations and boundaries of phase-lock areas in a model of overdamped Josephson effect”, Proc. Steklov Inst. Math., 297 (2017), 50–89
Glutsyuk A., Rybnikov L., “On Families of Differential Equations on Two-Torus With All Phase-Lock Areas”, Nonlinearity, 30:1 (2017), 61–72
I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Sluchai Gessa–Appelrota i kvantovanie chisla vrascheniya”, Nelineinaya dinam., 13:3 (2017), 433–452
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Hess–Appelrot Case and Quantization of the Rotation Number”, Regul. Chaotic Dyn., 22:2 (2017), 180–196
Buchstaber V.M. Glutsyuk A.A., “On determinants of modified Bessel functions and entire solutions of double confluent Heun equations”, Nonlinearity, 29:12 (2016), 3857–3870
V. M. Buchstaber, S. I. Tertychnyi, “Holomorphic solutions of the double confluent Heun equation associated with the RSJ model of the Josephson junction”, Theoret. and Math. Phys., 182:3 (2015), 329–355
A. Klimenko, O. Romaskevich, “Asymptotic properties of Arnold tongues and Josephson effect”, Mosc. Math. J., 14:2 (2014), 367–384
A. A. Glutsyuk, V. A. Kleptsyn, D. A. Filimonov, I. V. Shchurov, “On the Adjacency Quantization in an Equation Modeling the Josephson Effect”, Funct. Anal. Appl., 48:4 (2014), 272–285

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

Statistics & downloads:
Abstract page:	956
Full-text PDF :	319
References:	102
First page:	26

Что такое QR-код?

Registration to the website

Logotypes