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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 23 scientific papers (total in 23 papers)

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

Yu. S. Ilyashenkoabcd, D. A. Ryzhove, D. A. Filimonovf

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 (23)
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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
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    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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