TY  - JOUR
AU  - Odavic, Jovan
AU  - Mali, Petar
AU  - Tekić, Jasmina
AU  - Pantic, Milan
AU  - Pavkov-Hrvojević, Milica
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1413
AB  - Dynamics of driven dissipative Frenkel-Kontorova model is examined by using largest Lyapunov exponent computational technique. Obtained results show that besides the usual way where behavior of the system in the presence of external forces is studied by analyzing its dynamical response function, the largest Lyapunov exponent analysis can represent a very convenient tool to examine system dynamics. In the dc driven systems, the critical depinning force for particular structure could be estimated by computing the largest Lyapunov exponent. In the dc+ac driven systems, if the substrate potential is the standard sinusoidal one, calculation of the largest Lyapunov exponent offers a more sensitive way to detect the presence of Shapiro steps. When the amplitude of the ac force is varied the behavior of the largest Lyapunov exponent in the pinned regime completely reflects the behavior of Shapiro steps and the critical depinning force, in particular, it represents the mirror image of the amplitude dependence of critical depinning force. This points out an advantage of this technique since by calculating the largest Lyapunov exponent in the pinned regime we can get an insight into the dynamics of the system when driving forces are applied. Additionally, the system is shown to be not chaotic even in the case of incommensurate structures and large amplitudes of external force, which is a consequence of overdampness of the model and the Middletons no passing rule. (C) 2016 Elsevier B.V. All rights reserved.
T2  - Communications in Nonlinear Science and Numerical Simulation
T1  - Application of largest Lyapunov exponent analysis on the studies of dynamics under external forces
VL  - 47
SP  - 100
EP  - 108
DO  - 10.1016/j.cnsns.2016.11.010
ER  - 

@article{
author = "Odavic, Jovan and Mali, Petar and Tekić, Jasmina and Pantic, Milan and Pavkov-Hrvojević, Milica",
year = "2017",
abstract = "Dynamics of driven dissipative Frenkel-Kontorova model is examined by using largest Lyapunov exponent computational technique. Obtained results show that besides the usual way where behavior of the system in the presence of external forces is studied by analyzing its dynamical response function, the largest Lyapunov exponent analysis can represent a very convenient tool to examine system dynamics. In the dc driven systems, the critical depinning force for particular structure could be estimated by computing the largest Lyapunov exponent. In the dc+ac driven systems, if the substrate potential is the standard sinusoidal one, calculation of the largest Lyapunov exponent offers a more sensitive way to detect the presence of Shapiro steps. When the amplitude of the ac force is varied the behavior of the largest Lyapunov exponent in the pinned regime completely reflects the behavior of Shapiro steps and the critical depinning force, in particular, it represents the mirror image of the amplitude dependence of critical depinning force. This points out an advantage of this technique since by calculating the largest Lyapunov exponent in the pinned regime we can get an insight into the dynamics of the system when driving forces are applied. Additionally, the system is shown to be not chaotic even in the case of incommensurate structures and large amplitudes of external force, which is a consequence of overdampness of the model and the Middletons no passing rule. (C) 2016 Elsevier B.V. All rights reserved.",
journal = "Communications in Nonlinear Science and Numerical Simulation",
title = "Application of largest Lyapunov exponent analysis on the studies of dynamics under external forces",
volume = "47",
pages = "100-108",
doi = "10.1016/j.cnsns.2016.11.010"
}

Odavic, J., Mali, P., Tekić, J., Pantic, M.,& Pavkov-Hrvojević, M.. (2017). Application of largest Lyapunov exponent analysis on the studies of dynamics under external forces. in Communications in Nonlinear Science and Numerical Simulation, 47, 100-108.
https://doi.org/10.1016/j.cnsns.2016.11.010

Odavic J, Mali P, Tekić J, Pantic M, Pavkov-Hrvojević M. Application of largest Lyapunov exponent analysis on the studies of dynamics under external forces. in Communications in Nonlinear Science and Numerical Simulation. 2017;47:100-108.
doi:10.1016/j.cnsns.2016.11.010 .

Odavic, Jovan, Mali, Petar, Tekić, Jasmina, Pantic, Milan, Pavkov-Hrvojević, Milica, "Application of largest Lyapunov exponent analysis on the studies of dynamics under external forces" in Communications in Nonlinear Science and Numerical Simulation, 47 (2017):100-108,
https://doi.org/10.1016/j.cnsns.2016.11.010 . .

TY  - JOUR
AU  - Odavic, Jovan
AU  - Mali, Petar
AU  - Tekić, Jasmina
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/531
AB  - 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.
T2  - Physical Review E
T1  - Farey sequence in the appearance of subharmonic Shapiro steps
VL  - 91
IS  - 5
DO  - 10.1103/PhysRevE.91.052904
ER  - 

@article{
author = "Odavic, Jovan and Mali, Petar and Tekić, Jasmina",
year = "2015",
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.",
journal = "Physical Review E",
title = "Farey sequence in the appearance of subharmonic Shapiro steps",
volume = "91",
number = "5",
doi = "10.1103/PhysRevE.91.052904"
}

Odavic, J., Mali, P.,& Tekić, J.. (2015). Farey sequence in the appearance of subharmonic Shapiro steps. in Physical Review E, 91(5).
https://doi.org/10.1103/PhysRevE.91.052904

Odavic J, Mali P, Tekić J. Farey sequence in the appearance of subharmonic Shapiro steps. in Physical Review E. 2015;91(5).
doi:10.1103/PhysRevE.91.052904 .

Odavic, Jovan, Mali, Petar, Tekić, Jasmina, "Farey sequence in the appearance of subharmonic Shapiro steps" in Physical Review E, 91, no. 5 (2015),
https://doi.org/10.1103/PhysRevE.91.052904 . .