TY  - JOUR
AU  - Mali, Petar
AU  - Šakota, Anđela
AU  - Tekić, Jasmina
AU  - Radošević, Slobodan
AU  - Pantić, Milan
AU  - Pavkov-Hrvojević, Milica
PY  - 2020
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8931
AB  - We demonstrate, using the example of the dc+ac driven overdamped Frenkel-Kontorova model, that an easily calculable measure of complexity can be used for the examination of Shapiro steps in the presence of thermal noise. In real systems, thermal noise causes melting or even disappearance of Shapiro steps, which makes their analysis in the standard way from the response function difficult. Unlike in the conventional approach, here, by calculating the Kolmogorov complexity of certain areas in the response function, we were able to detect Shapiro steps, measure their size with the desired precision, and examine their temperature dependence. The aim of this work is to provide scientists, particularly experimentalists, with an unconventional, but practical and easy tool for examination of Shapiro steps in real systems.
T2  - Physical Review E
T1  - Complexity of Shapiro steps
VL  - 101
IS  - 3
SP  - 032203
DO  - 10.1103/PhysRevE.101.032203
ER  - 

@article{
author = "Mali, Petar and Šakota, Anđela and Tekić, Jasmina and Radošević, Slobodan and Pantić, Milan and Pavkov-Hrvojević, Milica",
year = "2020",
abstract = "We demonstrate, using the example of the dc+ac driven overdamped Frenkel-Kontorova model, that an easily calculable measure of complexity can be used for the examination of Shapiro steps in the presence of thermal noise. In real systems, thermal noise causes melting or even disappearance of Shapiro steps, which makes their analysis in the standard way from the response function difficult. Unlike in the conventional approach, here, by calculating the Kolmogorov complexity of certain areas in the response function, we were able to detect Shapiro steps, measure their size with the desired precision, and examine their temperature dependence. The aim of this work is to provide scientists, particularly experimentalists, with an unconventional, but practical and easy tool for examination of Shapiro steps in real systems.",
journal = "Physical Review E",
title = "Complexity of Shapiro steps",
volume = "101",
number = "3",
pages = "032203",
doi = "10.1103/PhysRevE.101.032203"
}

Mali, P., Šakota, A., Tekić, J., Radošević, S., Pantić, M.,& Pavkov-Hrvojević, M.. (2020). Complexity of Shapiro steps. in Physical Review E, 101(3), 032203.
https://doi.org/10.1103/PhysRevE.101.032203

Mali P, Šakota A, Tekić J, Radošević S, Pantić M, Pavkov-Hrvojević M. Complexity of Shapiro steps. in Physical Review E. 2020;101(3):032203.
doi:10.1103/PhysRevE.101.032203 .

Mali, Petar, Šakota, Anđela, Tekić, Jasmina, Radošević, Slobodan, Pantić, Milan, Pavkov-Hrvojević, Milica, "Complexity of Shapiro steps" in Physical Review E, 101, no. 3 (2020):032203,
https://doi.org/10.1103/PhysRevE.101.032203 . .

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 . .