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  - Mali, Petar
AU  - Tekić, Jasmina
AU  - Pantic, Milan
PY  - 2014
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/6002
AB  - Properties of the Shapiro steps in different commensurate structures of the ac + dc driven Frenkel-Kontorova model with asymmetric deformable substrate potential have been examined. Deviation from the sinusoidal potential produces appearance of large subharmonic steps. In general, different commensurate structures respond differently to the applied force and have different velocities. The results have shown that after shape parameter gets some critical value, there is no difference in the behavior of Shapiro steps for different commensurate structures. The step size and the critical depinning force for different commensurate structures saturate to the same values, due to reduction of degrees of freedom with the large deformation of potential. (C) 2014 Elsevier B.V. All rights reserved.
T2  - Communications in Nonlinear Science and Numerical Simulation
T1  - Saturation effects in ac plus dc driven Frenkel-Kontorova model
VL  - 19
IS  - 10
SP  - 3469
EP  - 3475
DO  - 10.1016/j.cnsns.2014.03.017
ER  - 

@article{
author = "Mali, Petar and Tekić, Jasmina and Pantic, Milan",
year = "2014",
abstract = "Properties of the Shapiro steps in different commensurate structures of the ac + dc driven Frenkel-Kontorova model with asymmetric deformable substrate potential have been examined. Deviation from the sinusoidal potential produces appearance of large subharmonic steps. In general, different commensurate structures respond differently to the applied force and have different velocities. The results have shown that after shape parameter gets some critical value, there is no difference in the behavior of Shapiro steps for different commensurate structures. The step size and the critical depinning force for different commensurate structures saturate to the same values, due to reduction of degrees of freedom with the large deformation of potential. (C) 2014 Elsevier B.V. All rights reserved.",
journal = "Communications in Nonlinear Science and Numerical Simulation",
title = "Saturation effects in ac plus dc driven Frenkel-Kontorova model",
volume = "19",
number = "10",
pages = "3469-3475",
doi = "10.1016/j.cnsns.2014.03.017"
}

Mali, P., Tekić, J.,& Pantic, M.. (2014). Saturation effects in ac plus dc driven Frenkel-Kontorova model. in Communications in Nonlinear Science and Numerical Simulation, 19(10), 3469-3475.
https://doi.org/10.1016/j.cnsns.2014.03.017

Mali P, Tekić J, Pantic M. Saturation effects in ac plus dc driven Frenkel-Kontorova model. in Communications in Nonlinear Science and Numerical Simulation. 2014;19(10):3469-3475.
doi:10.1016/j.cnsns.2014.03.017 .

Mali, Petar, Tekić, Jasmina, Pantic, Milan, "Saturation effects in ac plus dc driven Frenkel-Kontorova model" in Communications in Nonlinear Science and Numerical Simulation, 19, no. 10 (2014):3469-3475,
https://doi.org/10.1016/j.cnsns.2014.03.017 . .

TY  - JOUR
AU  - Mali, Petar
AU  - Tekić, Jasmina
AU  - Ivić, Zoran
AU  - Pantic, Milan
PY  - 2012
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5102
AB  - Existence and properties of the Shapiro steps in the presence of noise have been studied in the ac driven overdamped Frenkel-Kontorova model with deformable substrate potential. The results have shown that the influence of noise on interference phenomena is determined by the presence and the size of half-integer steps. Since half-integer steps are more affected by noise, and the properties of harmonic steps are directly correlated with the size of half-integer steps, noise will have completely different effects on the harmonic steps if half-integer steps are present. As temperature increases, in the amplitude dependence of the step width, deviation from the well-known Bessel-like oscillations has been observed, and three different types of behavior have been classified. In the influence of noise on the frequency dependence of the steps, appearance of oscillations and strong influence of half-integer steps on their form have been observed.
T2  - Physical Review E
T1  - Effects of noise on interference phenomena in the presence of subharmonic Shapiro steps
VL  - 86
IS  - 4
DO  - 10.1103/PhysRevE.86.046209
ER  - 

@article{
author = "Mali, Petar and Tekić, Jasmina and Ivić, Zoran and Pantic, Milan",
year = "2012",
abstract = "Existence and properties of the Shapiro steps in the presence of noise have been studied in the ac driven overdamped Frenkel-Kontorova model with deformable substrate potential. The results have shown that the influence of noise on interference phenomena is determined by the presence and the size of half-integer steps. Since half-integer steps are more affected by noise, and the properties of harmonic steps are directly correlated with the size of half-integer steps, noise will have completely different effects on the harmonic steps if half-integer steps are present. As temperature increases, in the amplitude dependence of the step width, deviation from the well-known Bessel-like oscillations has been observed, and three different types of behavior have been classified. In the influence of noise on the frequency dependence of the steps, appearance of oscillations and strong influence of half-integer steps on their form have been observed.",
journal = "Physical Review E",
title = "Effects of noise on interference phenomena in the presence of subharmonic Shapiro steps",
volume = "86",
number = "4",
doi = "10.1103/PhysRevE.86.046209"
}

Mali, P., Tekić, J., Ivić, Z.,& Pantic, M.. (2012). Effects of noise on interference phenomena in the presence of subharmonic Shapiro steps. in Physical Review E, 86(4).
https://doi.org/10.1103/PhysRevE.86.046209

Mali P, Tekić J, Ivić Z, Pantic M. Effects of noise on interference phenomena in the presence of subharmonic Shapiro steps. in Physical Review E. 2012;86(4).
doi:10.1103/PhysRevE.86.046209 .

Mali, Petar, Tekić, Jasmina, Ivić, Zoran, Pantic, Milan, "Effects of noise on interference phenomena in the presence of subharmonic Shapiro steps" in Physical Review E, 86, no. 4 (2012),
https://doi.org/10.1103/PhysRevE.86.046209 . .