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This article is cited in 11 scientific papers (total in 11 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.
Received: June 26, 2013; in revised form December 6, 2013
Citation:
A. Klimenko, O. Romaskevich, “Asymptotic properties of Arnold tongues and Josephson effect”, Mosc. Math. J., 14:2 (2014), 367–384
Linking options:
https://www.mathnet.ru/eng/mmj526 https://www.mathnet.ru/eng/mmj/v14/i2/p367
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