title: Farey sequence in the appearance of subharmonic Shapiro steps.
abstract: The largest Lyapunov exponent has been examined in the dynamical-mode locking phenomena of the ac+dc driven dissipative Frenkel-Kontorova model with deformable substrate potential. Due to deformation, large fractional and higher order subharmonic steps appear in the response function of the system. Computation of the largest Lyapunov exponent as a way to verify their presence led to the observation of the Farey sequence. In the standard regime, the appearance of half-integer and other subharmonic steps between the large harmonic steps, and their relative sizes follow the Farey construction. In the nonstandard regime, however, the half-integer steps are larger than harmonic ones, and Farey construction is only present in the appearance of higher order subharmonic steps. The examination of Lyapunov exponents has also shown that regardless of the substrate potential or deformation, there was no chaos in the system.
authors.affiliation: Institut für Theorie der Statistishen Physik-RWTH Aachen University, Peter-Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich, Germany.
authors.forename: Jovan
authors.initials: J
authors.lastname: Odavić
authors.affiliation: Department of Physics, Faculty of Science, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia.
authors.forename: Petar
authors.initials: P
authors.lastname: Mali
authors.affiliation: "Vinča" Institute of Nuclear Sciences, Laboratory for Theoretical and Condensed Matter Physics 020, University of Belgrade, P.O. Box 522, 11001 Belgrade, Serbia.
authors.forename: Jasmina
authors.initials: J
authors.lastname: Tekić