TY  - JOUR
AU  - Mali, Petar
AU  - Radošević, Slobodan
AU  - Gombar, Sonja
AU  - Tekić, Jasmina
AU  - Pantić, Milan
AU  - Pavkov-Hrvojević, Milica
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/11214
AB  - Dynamics of the driven Frenkel-Kontorova model with asymmetric deformable substrate potential is examined by analyzing response function, the largest Lyapunov exponent, and Poincaré sections for two neighboring particles. The obtained results show that the largest Lyapunov exponent, besides being used for investigating integral quantities, can be used for detecting microchanges in chain configuration of both damped Frenkel-Kontorova model with inertial term and its strictly overdamped limit. Slight changes in relative positions of the particles are registered through jumps of the largest Lyapunov exponent in the pinning regime. The occurrence of such jumps is highly dependent on type of commensurate structure and deformation of substrate potential. The obtained results also show that the minimal force required to initiate collective motion of the chain is not dependent on the number of Lyapunov exponent jumps in the pinning regime. These jumps are also registered in the sliding regime, where they are a consequence of a more complex structure of largest Lyapunov exponent on the step. © 2023 American Physical Society.
T2  - Physical Review E
T1  - Largest Lyapunov exponent as a tool for detecting relative changes in the particle positions
VL  - 107
IS  - 6
SP  - 064213
DO  - 10.1103/PhysRevE.107.064213
ER  - 

@article{
author = "Mali, Petar and Radošević, Slobodan and Gombar, Sonja and Tekić, Jasmina and Pantić, Milan and Pavkov-Hrvojević, Milica",
year = "2023",
abstract = "Dynamics of the driven Frenkel-Kontorova model with asymmetric deformable substrate potential is examined by analyzing response function, the largest Lyapunov exponent, and Poincaré sections for two neighboring particles. The obtained results show that the largest Lyapunov exponent, besides being used for investigating integral quantities, can be used for detecting microchanges in chain configuration of both damped Frenkel-Kontorova model with inertial term and its strictly overdamped limit. Slight changes in relative positions of the particles are registered through jumps of the largest Lyapunov exponent in the pinning regime. The occurrence of such jumps is highly dependent on type of commensurate structure and deformation of substrate potential. The obtained results also show that the minimal force required to initiate collective motion of the chain is not dependent on the number of Lyapunov exponent jumps in the pinning regime. These jumps are also registered in the sliding regime, where they are a consequence of a more complex structure of largest Lyapunov exponent on the step. © 2023 American Physical Society.",
journal = "Physical Review E",
title = "Largest Lyapunov exponent as a tool for detecting relative changes in the particle positions",
volume = "107",
number = "6",
pages = "064213",
doi = "10.1103/PhysRevE.107.064213"
}

Mali, P., Radošević, S., Gombar, S., Tekić, J., Pantić, M.,& Pavkov-Hrvojević, M.. (2023). Largest Lyapunov exponent as a tool for detecting relative changes in the particle positions. in Physical Review E, 107(6), 064213.
https://doi.org/10.1103/PhysRevE.107.064213

Mali P, Radošević S, Gombar S, Tekić J, Pantić M, Pavkov-Hrvojević M. Largest Lyapunov exponent as a tool for detecting relative changes in the particle positions. in Physical Review E. 2023;107(6):064213.
doi:10.1103/PhysRevE.107.064213 .

Mali, Petar, Radošević, Slobodan, Gombar, Sonja, Tekić, Jasmina, Pantić, Milan, Pavkov-Hrvojević, Milica, "Largest Lyapunov exponent as a tool for detecting relative changes in the particle positions" in Physical Review E, 107, no. 6 (2023):064213,
https://doi.org/10.1103/PhysRevE.107.064213 . .

TY  - CONF
AU  - Tekić, Jasmina
AU  - Botha, Andre
AU  - Mali, Petar
AU  - Shukrinov, Yuri M.
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10113
AB  - The appearance of devil’s staircase and chaos have been studied in the dc+ac driven Frenkel-Kontorova model. In the overdamped limit, the devil’s staircase structure arising from the complete mode-locking of an entirely nonchaotic system 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. When the inertial term is included, unlike in the overdamped case, the increase of mass led to the appearance of the whole series of subharmonic steps in the staircase of the average velocity as a function of average driving force in any commensurate structure. At certain values of parameters, the subharmonic steps became separated by chaotic windows while the whole structure retained scaling similar to the original staircase. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.
C3  - Springer Proceedings in Complexity
T1  - The AC Driven Frenkel-Kontorova Model: From Shapiro Steps to Chaos
SP  - 943
EP  - 951
DO  - 10.1007/978-3-030-70795-8_65
ER  - 

@conference{
author = "Tekić, Jasmina and Botha, Andre and Mali, Petar and Shukrinov, Yuri M.",
year = "2021",
abstract = "The appearance of devil’s staircase and chaos have been studied in the dc+ac driven Frenkel-Kontorova model. In the overdamped limit, the devil’s staircase structure arising from the complete mode-locking of an entirely nonchaotic system 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. When the inertial term is included, unlike in the overdamped case, the increase of mass led to the appearance of the whole series of subharmonic steps in the staircase of the average velocity as a function of average driving force in any commensurate structure. At certain values of parameters, the subharmonic steps became separated by chaotic windows while the whole structure retained scaling similar to the original staircase. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",
journal = "Springer Proceedings in Complexity",
title = "The AC Driven Frenkel-Kontorova Model: From Shapiro Steps to Chaos",
pages = "943-951",
doi = "10.1007/978-3-030-70795-8_65"
}

Tekić, J., Botha, A., Mali, P.,& Shukrinov, Y. M.. (2021). The AC Driven Frenkel-Kontorova Model: From Shapiro Steps to Chaos. in Springer Proceedings in Complexity, 943-951.
https://doi.org/10.1007/978-3-030-70795-8_65

Tekić J, Botha A, Mali P, Shukrinov YM. The AC Driven Frenkel-Kontorova Model: From Shapiro Steps to Chaos. in Springer Proceedings in Complexity. 2021;:943-951.
doi:10.1007/978-3-030-70795-8_65 .

Tekić, Jasmina, Botha, Andre, Mali, Petar, Shukrinov, Yuri M., "The AC Driven Frenkel-Kontorova Model: From Shapiro Steps to Chaos" in Springer Proceedings in Complexity (2021):943-951,
https://doi.org/10.1007/978-3-030-70795-8_65 . .

TY  - JOUR
AU  - Gombar, Sonja
AU  - Mali, Petar
AU  - Radošević, Slobodan
AU  - Tekić, Jasmina
AU  - Pantić, Milan
AU  - Pavkov-Hrvojević, Milica
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9518
AB  - The response function and largest Lyapunov exponent analysis were applied to the driven overdamped Frenkel-Kontorova model with two types of anharmonic convex interparticle potentials. In both cases model reduces to a single particle model for integer values of winding number. It is shown that the mirror image of the amplitude dependence of critical depinning force and largest Lyapunov exponent observed recently in the standard Frenkel-Kontorova model (Odavić et al 2017 Commun. Nonlinear Sci. Numer. Simul. 47, 100) is not retained generally. Behaviour of systems with relatively strong interparticle force was examined and evidence for the appearance of mode-locking phenomenon in both directions of particles’ motion is presented. © 2021 IOP Publishing Ltd.
T2  - Physica Scripta
T1  - Influence of anharmonic convex interparticle potential and Shapiro steps in the opposite direction of driving force
VL  - 96
IS  - 3
SP  - 035211
DO  - 10.1088/1402-4896/abd5ec
ER  - 

@article{
author = "Gombar, Sonja and Mali, Petar and Radošević, Slobodan and Tekić, Jasmina and Pantić, Milan and Pavkov-Hrvojević, Milica",
year = "2021",
abstract = "The response function and largest Lyapunov exponent analysis were applied to the driven overdamped Frenkel-Kontorova model with two types of anharmonic convex interparticle potentials. In both cases model reduces to a single particle model for integer values of winding number. It is shown that the mirror image of the amplitude dependence of critical depinning force and largest Lyapunov exponent observed recently in the standard Frenkel-Kontorova model (Odavić et al 2017 Commun. Nonlinear Sci. Numer. Simul. 47, 100) is not retained generally. Behaviour of systems with relatively strong interparticle force was examined and evidence for the appearance of mode-locking phenomenon in both directions of particles’ motion is presented. © 2021 IOP Publishing Ltd.",
journal = "Physica Scripta",
title = "Influence of anharmonic convex interparticle potential and Shapiro steps in the opposite direction of driving force",
volume = "96",
number = "3",
pages = "035211",
doi = "10.1088/1402-4896/abd5ec"
}

Gombar, S., Mali, P., Radošević, S., Tekić, J., Pantić, M.,& Pavkov-Hrvojević, M.. (2021). Influence of anharmonic convex interparticle potential and Shapiro steps in the opposite direction of driving force. in Physica Scripta, 96(3), 035211.
https://doi.org/10.1088/1402-4896/abd5ec

Gombar S, Mali P, Radošević S, Tekić J, Pantić M, Pavkov-Hrvojević M. Influence of anharmonic convex interparticle potential and Shapiro steps in the opposite direction of driving force. in Physica Scripta. 2021;96(3):035211.
doi:10.1088/1402-4896/abd5ec .

Gombar, Sonja, Mali, Petar, Radošević, Slobodan, Tekić, Jasmina, Pantić, Milan, Pavkov-Hrvojević, Milica, "Influence of anharmonic convex interparticle potential and Shapiro steps in the opposite direction of driving force" in Physica Scripta, 96, no. 3 (2021):035211,
https://doi.org/10.1088/1402-4896/abd5ec . .

TY  - JOUR
AU  - Rahmonov, Ilhom R.
AU  - Tekić, Jasmina
AU  - Mali, Petar
AU  - Irie, Akinobu
AU  - Shukrinov, Yury M.
PY  - 2020
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8809
AB  - Examination of an annular system of underdamped Josephson junctions in the presence of external radiation showed that the ability of the system to lock with some external radiation was determined not only by the number but also by the type of rotating excitations (fluxons or antifluxons). Shapiro steps can be observed in the current-voltage characteristic only in the system with trapped fluxons or in the system with fluxon-antifluxon pairs. If the trapped fluxons circulate simultaneously with fluxon-antifluxon pairs, there are no Shapiro steps regardless of the amplitude or frequency of the applied external radiation. © 2020 American Physical Society.
T2  - Physical Review B
T1  - Ac-driven annular Josephson junctions: The missing Shapiro steps
VL  - 101
IS  - 2
SP  - 024512
DO  - 10.1103/PhysRevB.101.024512
ER  - 

@article{
author = "Rahmonov, Ilhom R. and Tekić, Jasmina and Mali, Petar and Irie, Akinobu and Shukrinov, Yury M.",
year = "2020",
abstract = "Examination of an annular system of underdamped Josephson junctions in the presence of external radiation showed that the ability of the system to lock with some external radiation was determined not only by the number but also by the type of rotating excitations (fluxons or antifluxons). Shapiro steps can be observed in the current-voltage characteristic only in the system with trapped fluxons or in the system with fluxon-antifluxon pairs. If the trapped fluxons circulate simultaneously with fluxon-antifluxon pairs, there are no Shapiro steps regardless of the amplitude or frequency of the applied external radiation. © 2020 American Physical Society.",
journal = "Physical Review B",
title = "Ac-driven annular Josephson junctions: The missing Shapiro steps",
volume = "101",
number = "2",
pages = "024512",
doi = "10.1103/PhysRevB.101.024512"
}

Rahmonov, I. R., Tekić, J., Mali, P., Irie, A.,& Shukrinov, Y. M.. (2020). Ac-driven annular Josephson junctions: The missing Shapiro steps. in Physical Review B, 101(2), 024512.
https://doi.org/10.1103/PhysRevB.101.024512

Rahmonov IR, Tekić J, Mali P, Irie A, Shukrinov YM. Ac-driven annular Josephson junctions: The missing Shapiro steps. in Physical Review B. 2020;101(2):024512.
doi:10.1103/PhysRevB.101.024512 .

Rahmonov, Ilhom R., Tekić, Jasmina, Mali, Petar, Irie, Akinobu, Shukrinov, Yury M., "Ac-driven annular Josephson junctions: The missing Shapiro steps" in Physical Review B, 101, no. 2 (2020):024512,
https://doi.org/10.1103/PhysRevB.101.024512 . .

TY  - JOUR
AU  - Rahmonov, Ilhom R.
AU  - Tekić, Jasmina
AU  - Mali, Petar
AU  - Irie, Akinobu
AU  - Plecenik, Anrej
AU  - Shukrinov, Yu. M.
PY  - 2020
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9634
AB  - The appearance and origin of resonance phenomena are studied in an annular system of underdamped Josephson junctions. If no fluxon is trapped in the system, the dynamics is governed by the motion of fluxon-antifluxon pairs. If, on the other hand, trapped fluxons are present, in addition to their motion, the system can also exhibit the simultaneous motion of trapped fluxons and fluxon-antifluxon pairs. Locking between the rotating excitations (fluxons and antifluxons) and the Josephson frequency leads to the appearance of zero-field steps in the current-voltage characteristics, whose number is determined by the number of junctions and the total number of excitations present in the system. The obtained results clearly show that the branching of zero-field steps due to resonance between the rotating excitations and plasma oscillations in their tails appears only at the lower steps and completely disappears at the higher steps. A comparative analysis between systems without and those with trapped fluxons shows a correlation between their current-voltage characteristics. From a high-resolution analysis some special features of zero-field steps emerge such as an additional branch due to resonance between the pulsating fluxon and the Josephson frequency. Examination of systems with the same number but different types of excitations further reveals that their dynamics is determined not only by the number, but also by the type of excitations, i.e., systems with the same number but different types of excitations have different current-voltage characteristics. © 2020 American Physical Society.
T2  - Physical Review B
T1  - Resonance phenomena in an annular array of underdamped Josephson junctions
VL  - 101
IS  - 17
DO  - 10.1103/PHYSREVB.101.174515
ER  - 

@article{
author = "Rahmonov, Ilhom R. and Tekić, Jasmina and Mali, Petar and Irie, Akinobu and Plecenik, Anrej and Shukrinov, Yu. M.",
year = "2020",
abstract = "The appearance and origin of resonance phenomena are studied in an annular system of underdamped Josephson junctions. If no fluxon is trapped in the system, the dynamics is governed by the motion of fluxon-antifluxon pairs. If, on the other hand, trapped fluxons are present, in addition to their motion, the system can also exhibit the simultaneous motion of trapped fluxons and fluxon-antifluxon pairs. Locking between the rotating excitations (fluxons and antifluxons) and the Josephson frequency leads to the appearance of zero-field steps in the current-voltage characteristics, whose number is determined by the number of junctions and the total number of excitations present in the system. The obtained results clearly show that the branching of zero-field steps due to resonance between the rotating excitations and plasma oscillations in their tails appears only at the lower steps and completely disappears at the higher steps. A comparative analysis between systems without and those with trapped fluxons shows a correlation between their current-voltage characteristics. From a high-resolution analysis some special features of zero-field steps emerge such as an additional branch due to resonance between the pulsating fluxon and the Josephson frequency. Examination of systems with the same number but different types of excitations further reveals that their dynamics is determined not only by the number, but also by the type of excitations, i.e., systems with the same number but different types of excitations have different current-voltage characteristics. © 2020 American Physical Society.",
journal = "Physical Review B",
title = "Resonance phenomena in an annular array of underdamped Josephson junctions",
volume = "101",
number = "17",
doi = "10.1103/PHYSREVB.101.174515"
}

Rahmonov, I. R., Tekić, J., Mali, P., Irie, A., Plecenik, A.,& Shukrinov, Yu. M.. (2020). Resonance phenomena in an annular array of underdamped Josephson junctions. in Physical Review B, 101(17).
https://doi.org/10.1103/PHYSREVB.101.174515

Rahmonov IR, Tekić J, Mali P, Irie A, Plecenik A, Shukrinov YM. Resonance phenomena in an annular array of underdamped Josephson junctions. in Physical Review B. 2020;101(17).
doi:10.1103/PHYSREVB.101.174515 .

Rahmonov, Ilhom R., Tekić, Jasmina, Mali, Petar, Irie, Akinobu, Plecenik, Anrej, Shukrinov, Yu. M., "Resonance phenomena in an annular array of underdamped Josephson junctions" in Physical Review B, 101, no. 17 (2020),
https://doi.org/10.1103/PHYSREVB.101.174515 . .

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  - Tekić, Jasmina
AU  - Botha, Andre E.
AU  - Mali, Petar
AU  - Shukrinov, Yury M.
PY  - 2019
UR  - https://link.aps.org/doi/10.1103/PhysRevE.99.022206
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8058
AB  - The effects of inertial terms on the dynamics of the dc+ac driven Frenkel-Kontorova model were examined. As the mass of particles was varied, the response of the system to the driving forces and appearance of the Shapiro steps were analyzed in detail. Unlike in the overdamped case, the increase of mass led to the appearance of the whole series of subharmonic steps in the staircase of the average velocity as a function of average driving force in any commensurate structure. At certain values of parameters, the subharmonic steps became separated by chaotic windows while the whole structure retained scaling similar to the original staircase. The mass of the particles also determined their sensitivity to the forces governing their dynamics. Depending on their mass, they were found to exhibit three types of dynamics, from dynamical mode-locking with chaotic windows, through to a typical dc response, to essentially a free-particle response. Examination of this dynamics in both the upforce and downforce directions showed that the system may not only exhibit hysteresis, but also that large Shapiro steps may appear in the downforce direction, even in cases for which no dynamical mode-locking occurred in the upforce direction. © 2019 American Physical Society.
T2  - Physical Review E
T1  - Inertial effects in the dc+ac driven underdamped Frenkel-Kontorova model: Subharmonic steps, chaos, and hysteresis
VL  - 99
IS  - 2
SP  - 022206
DO  - 10.1103/PhysRevE.99.022206
ER  - 

@article{
author = "Tekić, Jasmina and Botha, Andre E. and Mali, Petar and Shukrinov, Yury M.",
year = "2019",
abstract = "The effects of inertial terms on the dynamics of the dc+ac driven Frenkel-Kontorova model were examined. As the mass of particles was varied, the response of the system to the driving forces and appearance of the Shapiro steps were analyzed in detail. Unlike in the overdamped case, the increase of mass led to the appearance of the whole series of subharmonic steps in the staircase of the average velocity as a function of average driving force in any commensurate structure. At certain values of parameters, the subharmonic steps became separated by chaotic windows while the whole structure retained scaling similar to the original staircase. The mass of the particles also determined their sensitivity to the forces governing their dynamics. Depending on their mass, they were found to exhibit three types of dynamics, from dynamical mode-locking with chaotic windows, through to a typical dc response, to essentially a free-particle response. Examination of this dynamics in both the upforce and downforce directions showed that the system may not only exhibit hysteresis, but also that large Shapiro steps may appear in the downforce direction, even in cases for which no dynamical mode-locking occurred in the upforce direction. © 2019 American Physical Society.",
journal = "Physical Review E",
title = "Inertial effects in the dc+ac driven underdamped Frenkel-Kontorova model: Subharmonic steps, chaos, and hysteresis",
volume = "99",
number = "2",
pages = "022206",
doi = "10.1103/PhysRevE.99.022206"
}

Tekić, J., Botha, A. E., Mali, P.,& Shukrinov, Y. M.. (2019). Inertial effects in the dc+ac driven underdamped Frenkel-Kontorova model: Subharmonic steps, chaos, and hysteresis. in Physical Review E, 99(2), 022206.
https://doi.org/10.1103/PhysRevE.99.022206

Tekić J, Botha AE, Mali P, Shukrinov YM. Inertial effects in the dc+ac driven underdamped Frenkel-Kontorova model: Subharmonic steps, chaos, and hysteresis. in Physical Review E. 2019;99(2):022206.
doi:10.1103/PhysRevE.99.022206 .

Tekić, Jasmina, Botha, Andre E., Mali, Petar, Shukrinov, Yury M., "Inertial effects in the dc+ac driven underdamped Frenkel-Kontorova model: Subharmonic steps, chaos, and hysteresis" in Physical Review E, 99, no. 2 (2019):022206,
https://doi.org/10.1103/PhysRevE.99.022206 . .

TY  - JOUR
AU  - Sokolović, I.
AU  - Mali, Petar
AU  - Odavić, Jovan
AU  - Radošević, Slobodan M.
AU  - Medvedeva, S. Yu.
AU  - Botha, Andre E.
AU  - Shukrinov, Yury M.
AU  - Tekić, Jasmina
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1692
AB  - The devils 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.
T2  - Physical Review E
T1  - Devils staircase and the absence of chaos in the dc- and ac-driven overdamped Frenkel-Kontorova model
VL  - 96
IS  - 2
DO  - 10.1103/PhysRevE.96.022210
ER  - 

@article{
author = "Sokolović, I. and Mali, Petar and Odavić, Jovan and Radošević, Slobodan M. and Medvedeva, S. Yu. and Botha, Andre E. and Shukrinov, Yury M. and Tekić, Jasmina",
year = "2017",
abstract = "The devils 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.",
journal = "Physical Review E",
title = "Devils staircase and the absence of chaos in the dc- and ac-driven overdamped Frenkel-Kontorova model",
volume = "96",
number = "2",
doi = "10.1103/PhysRevE.96.022210"
}

Sokolović, I., Mali, P., Odavić, J., Radošević, S. M., Medvedeva, S. Yu., Botha, A. E., Shukrinov, Y. M.,& Tekić, J.. (2017). Devils staircase and the absence of chaos in the dc- and ac-driven overdamped Frenkel-Kontorova model. in Physical Review E, 96(2).
https://doi.org/10.1103/PhysRevE.96.022210

Sokolović I, Mali P, Odavić J, Radošević SM, Medvedeva SY, Botha AE, Shukrinov YM, Tekić J. Devils staircase and the absence of chaos in the dc- and ac-driven overdamped Frenkel-Kontorova model. in Physical Review E. 2017;96(2).
doi:10.1103/PhysRevE.96.022210 .

Sokolović, I., Mali, Petar, Odavić, Jovan, Radošević, Slobodan M., Medvedeva, S. Yu., Botha, Andre E., Shukrinov, Yury M., Tekić, Jasmina, "Devils staircase and the absence of chaos in the dc- and ac-driven overdamped Frenkel-Kontorova model" in Physical Review E, 96, no. 2 (2017),
https://doi.org/10.1103/PhysRevE.96.022210 . .

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 . .

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  - Tekić, Jasmina
AU  - Mali, Petar
AU  - Ivić, Zoran
AU  - Pantic, M.
PY  - 2013
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5769
AB  - Size effect of the subharmonic Shapiro steps on the behavior of harmonic ones is studied in the ac driven overdamped Frenkel-Kontorova model with different types of physically important realistic substrate potentials. The properties of harmonic Shapiro steps are directly correlated with the size of halfinteger steps; and according to that in their amplitude dependence, three distinctive types of behavior have been classified. Our results on other realistic systems show that these classifications are not universal, and that not only the size of halfinteger steps but also the type of the substrate potential determines the properties and correlation between the Shapiro steps. While for some potentials such as variable and double-barrier potential, system evolves through different types of amplitude dependence as the size of halfinteger steps changes, in the case of double-well potential, the system maintains the standard behavior (the behavior for small halfinteger steps) even in the presence of large halfinteger steps. (c) 2013 AIP Publishing LLC.
T2  - Journal of Applied Physics
T1  - Size effect of the subharmonic Shapiro steps on the interference phenomena in the Frenkel-Kontorova model with realistic substrate potentials
VL  - 114
IS  - 17
DO  - 10.1063/1.4829011
ER  - 

@article{
author = "Tekić, Jasmina and Mali, Petar and Ivić, Zoran and Pantic, M.",
year = "2013",
abstract = "Size effect of the subharmonic Shapiro steps on the behavior of harmonic ones is studied in the ac driven overdamped Frenkel-Kontorova model with different types of physically important realistic substrate potentials. The properties of harmonic Shapiro steps are directly correlated with the size of halfinteger steps; and according to that in their amplitude dependence, three distinctive types of behavior have been classified. Our results on other realistic systems show that these classifications are not universal, and that not only the size of halfinteger steps but also the type of the substrate potential determines the properties and correlation between the Shapiro steps. While for some potentials such as variable and double-barrier potential, system evolves through different types of amplitude dependence as the size of halfinteger steps changes, in the case of double-well potential, the system maintains the standard behavior (the behavior for small halfinteger steps) even in the presence of large halfinteger steps. (c) 2013 AIP Publishing LLC.",
journal = "Journal of Applied Physics",
title = "Size effect of the subharmonic Shapiro steps on the interference phenomena in the Frenkel-Kontorova model with realistic substrate potentials",
volume = "114",
number = "17",
doi = "10.1063/1.4829011"
}

Tekić, J., Mali, P., Ivić, Z.,& Pantic, M.. (2013). Size effect of the subharmonic Shapiro steps on the interference phenomena in the Frenkel-Kontorova model with realistic substrate potentials. in Journal of Applied Physics, 114(17).
https://doi.org/10.1063/1.4829011

Tekić J, Mali P, Ivić Z, Pantic M. Size effect of the subharmonic Shapiro steps on the interference phenomena in the Frenkel-Kontorova model with realistic substrate potentials. in Journal of Applied Physics. 2013;114(17).
doi:10.1063/1.4829011 .

Tekić, Jasmina, Mali, Petar, Ivić, Zoran, Pantic, M., "Size effect of the subharmonic Shapiro steps on the interference phenomena in the Frenkel-Kontorova model with realistic substrate potentials" in Journal of Applied Physics, 114, no. 17 (2013),
https://doi.org/10.1063/1.4829011 . .

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 . .