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https://open.uns.ac.rs/handle/123456789/18475
Title: | Devil's staircase and the absence of chaos in the dc- and ac-driven overdamped Frenkel-Kontorova model | Authors: | Sokolović Igor Mali Petar Jovan Odavic Radosevic Slobodan Medvedeva Svetlana Botha Andre Shukrinov Yuri Jasmina Tekic |
Issue Date: | 2017 | Journal: | Physical Review E | Abstract: | © 2017 American Physical Society. 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. | URI: | https://open.uns.ac.rs/handle/123456789/18475 | ISSN: | 2470-0045 | DOI: | 10.1103/PhysRevE.96.022210 |
Appears in Collections: | PMF Publikacije/Publications |
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