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Devil’s staircase and the absence of chaos in the dc- and ac-driven overdamped Frenkel-Kontorova modelстатья
Статья опубликована в высокорейтинговом журнале
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 29 марта 2018 г.
- Авторы: Sokolovic I., Mali P., Odavic J., Radosevic S., Medvedeva S.Yu, Botha A.E., Shukrinov Yu M., Tekic J.
- Журнал: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
- Том: 96
- Номер: 2
- Год издания: 2017
- Издательство: American Physical Society
- Местоположение издательства: United States
- Первая страница: 022210
- DOI: 10.1103/PhysRevE.96.022210
- Аннотация: The devil’s staircase structure arising from the complete mode locking of an entirely nonchaotic system, the overdamped dc+ac driven Frenkel-Kontorova model with deformable substrate potential, was observed. Even though no chaos was found, a hierarchical ordering of the Shapiro steps was made possible through the use of a previously introduced continued fraction formula. The absence of chaos, deduced here from Lyapunov exponent analyses, can be attributed to the overdamped character and the Middleton no-passing rule. A comparative analysis of a one-dimensional stack of Josephson junctions confirmed the disappearance of chaos with increasing dissipation. Other common dynamic features were also identified through this comparison. A detailed analysis of the amplitude dependence of the Shapiro steps revealed that only for the case of a purely sinusoidal substrate potential did the relative sizes of the steps follow a Farey sequence. For nonsinusoidal (deformed) potentials, the symmetry of the Stern-Brocot tree, depicting all members of particular Farey sequence, was seen to be increasingly broken, with certain steps being more prominent and their relative sizes not following the Farey rule.
- Добавил в систему: Куприянов Михаил Юрьевич