Comparing the Finite-Difference Schemes in the Simulation of Shunted Josephson Junctions
The paper provides investigation of the numerical effects in finite-difference models of RLC-shunted circuit simulating Josephson junction. We study digital models of the circuit obtained by explicit, implicit and semi-explicit Euler methods. The Dormand-Prince 8 ODE solver is used for verification...
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doaj-2213ce180e1f462883e7da88c116430b2020-11-24T22:05:36ZengFRUCTProceedings of the XXth Conference of Open Innovations Association FRUCT2305-72542343-07372018-11-0160223300305Comparing the Finite-Difference Schemes in the Simulation of Shunted Josephson JunctionsValerii Y. Ostrovskii0Artur I. Karimov1Vyacheslav G. Rybin2Ekaterina E. Kopets3Denis N. Butusov4Saint Petersburg Electrotechnical University "LETI", Saint Petersburg, RussiaSaint Petersburg Electrotechnical University "LETI", Saint Petersburg, RussiaSaint Petersburg Electrotechnical University "LETI", Saint Petersburg, RussiaSaint Petersburg Electrotechnical University "LETI", Saint Petersburg, RussiaSaint Petersburg Electrotechnical University "LETI", Saint Petersburg, RussiaThe paper provides investigation of the numerical effects in finite-difference models of RLC-shunted circuit simulating Josephson junction. We study digital models of the circuit obtained by explicit, implicit and semi-explicit Euler methods. The Dormand-Prince 8 ODE solver is used for verification as a reference method. Two aspects of the RLC- shunted Josephson junction model are considered: the dynamical maps (two-dimensional bifurcation diagrams) and chaotic transients existing in the system within a certain parameter range. We show that both explicit and implicit Euler methods distort the dynamical properties, including stretching or compressing the dynamical maps and changing chaotic transient lifetime decay curve. Experiments demonstrate high reliability of the first-order Euler-Cromer method in simulation of the shunted Josephson junction model which yields data close to the reference data. Obtained results bring new accurate chaotic transient lifetime decay equation for the RLC-shunted Josephson junction model.https://fruct.org/publications/fruct23/files/Ost.pdf finite-difference schemedynamical systemJosephson junctionbifurcationchaotic transients |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Valerii Y. Ostrovskii Artur I. Karimov Vyacheslav G. Rybin Ekaterina E. Kopets Denis N. Butusov |
spellingShingle |
Valerii Y. Ostrovskii Artur I. Karimov Vyacheslav G. Rybin Ekaterina E. Kopets Denis N. Butusov Comparing the Finite-Difference Schemes in the Simulation of Shunted Josephson Junctions Proceedings of the XXth Conference of Open Innovations Association FRUCT finite-difference scheme dynamical system Josephson junction bifurcation chaotic transients |
author_facet |
Valerii Y. Ostrovskii Artur I. Karimov Vyacheslav G. Rybin Ekaterina E. Kopets Denis N. Butusov |
author_sort |
Valerii Y. Ostrovskii |
title |
Comparing the Finite-Difference Schemes in the Simulation of Shunted Josephson Junctions |
title_short |
Comparing the Finite-Difference Schemes in the Simulation of Shunted Josephson Junctions |
title_full |
Comparing the Finite-Difference Schemes in the Simulation of Shunted Josephson Junctions |
title_fullStr |
Comparing the Finite-Difference Schemes in the Simulation of Shunted Josephson Junctions |
title_full_unstemmed |
Comparing the Finite-Difference Schemes in the Simulation of Shunted Josephson Junctions |
title_sort |
comparing the finite-difference schemes in the simulation of shunted josephson junctions |
publisher |
FRUCT |
series |
Proceedings of the XXth Conference of Open Innovations Association FRUCT |
issn |
2305-7254 2343-0737 |
publishDate |
2018-11-01 |
description |
The paper provides investigation of the numerical effects in finite-difference models of RLC-shunted circuit simulating Josephson junction. We study digital models of the circuit obtained by explicit, implicit and semi-explicit Euler methods. The Dormand-Prince 8 ODE solver is used for verification as a reference method. Two aspects of the RLC- shunted Josephson junction model are considered: the dynamical maps (two-dimensional bifurcation diagrams) and chaotic transients existing in the system within a certain parameter range. We show that both explicit and implicit Euler methods distort the dynamical properties, including stretching or compressing the dynamical maps and changing chaotic transient lifetime decay curve. Experiments demonstrate high reliability of the first-order Euler-Cromer method in simulation of the shunted Josephson junction model which yields data close to the reference data. Obtained results bring new accurate chaotic transient lifetime decay equation for the RLC-shunted Josephson junction model. |
topic |
finite-difference scheme dynamical system Josephson junction bifurcation chaotic transients |
url |
https://fruct.org/publications/fruct23/files/Ost.pdf
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work_keys_str_mv |
AT valeriiyostrovskii comparingthefinitedifferenceschemesinthesimulationofshuntedjosephsonjunctions AT arturikarimov comparingthefinitedifferenceschemesinthesimulationofshuntedjosephsonjunctions AT vyacheslavgrybin comparingthefinitedifferenceschemesinthesimulationofshuntedjosephsonjunctions AT ekaterinaekopets comparingthefinitedifferenceschemesinthesimulationofshuntedjosephsonjunctions AT denisnbutusov comparingthefinitedifferenceschemesinthesimulationofshuntedjosephsonjunctions |
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1725825562112425984 |