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Mosc. Math. J., 2014, Volume 14, Number 2, Pages 367–384 (Mi mmj526)  

This article is cited in 5 scientific papers (total in 5 papers)

Asymptotic properties of Arnold tongues and Josephson effect

A. Klimenkoab, O. Romaskevichcb

a Steklov Mathematical Institute of RAS
b National Research University Higher School of Economics
c École Normale Supérieure de Lyon

Abstract: A three-parametrical family of ODEs on a torus arises from a model of Josephson effect in a resistive case when a Josephson junction is biased by a sinusoidal microwave current. We study asymptotics of Arnold tongues of this family on the parametric plane (the third parameter is fixed) and prove that the boundaries of the tongues are asymptotically close to Bessel functions.

Key words and phrases: Arnold tongues, Josephson effect, dynamical system on the torus, rotation number.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-33020-mol-a-ved
12-01-31241-mol-a
Supported by part by RFBR grants 12-01-31241-mol-a and 12-01-33020-mol-a-ved.


Full text: http://www.mathjournals.org/.../2014-014-002-009.html
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Document Type: Article
MSC: 37E45, 34E05
Received: June 26, 2013; in revised form December 6, 2013
Language: English

Citation: A. Klimenko, O. Romaskevich, “Asymptotic properties of Arnold tongues and Josephson effect”, Mosc. Math. J., 14:2 (2014), 367–384

Citation in format AMSBIB
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\by A.~Klimenko, O.~Romaskevich
\paper Asymptotic properties of Arnold tongues and Josephson effect
\jour Mosc. Math.~J.
\yr 2014
\vol 14
\issue 2
\pages 367--384
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3236498}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000342789300009}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    3. V. Kleptsyn, A. Okunev, I. Schurov, D. Zubov, M. I. Katsnelson, “Chiral tunneling through generic one-dimensional potential barriers in bilayer graphene”, Phys. Rev. B, 92:16 (2015), 165407  crossref  isi  elib  scopus
    4. V. M. Buchstaber, A. A. Glutsyuk, “On determinants of modified Bessel functions and entire solutions of double confluent Heun equations”, Nonlinearity, 29:12 (2016), 3857–3870  crossref  mathscinet  zmath  isi  scopus
    5. 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  mathnet  crossref  crossref  mathscinet  isi  elib
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