TY  - JOUR
AU  - Botha, Andre E.
AU  - Shukrinov, Yury M.
AU  - Tekić, Jasmina
AU  - Kolahchi, Mohammad R.
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10691
AB  - The ordinary (superconductor-insulator-superconductor) Josephson junction cannot exhibit chaos in the absence of an external ac drive, whereas in the superconductor-ferromagnet-superconductor Josephson junction, known as the φ0 junction, the magnetic layer effectively provides two extra degrees of freedom that can facilitate chaotic dynamics in the resulting four-dimensional autonomous system. In this work, we use the Landau-Lifshitz-Gilbert model for the magnetic moment of the ferromagnetic weak link, while the Josephson junction is described by the resistively capacitively shunted-junction model. We study the chaotic dynamics of the system for parameters surrounding the ferromagnetic resonance region, i.e., for which the Josephson frequency is reasonably close to the ferromagnetic frequency. We show that, due to the conservation of magnetic moment magnitude, two of the numerically computed full spectrum Lyapunov characteristic exponents are trivially zero. One-parameter bifurcation diagrams are used to investigate various transitions that occur between quasiperiodic, chaotic, and regular regions as the dc-bias current through the junction, I, is varied. We also compute two-dimensional bifurcation diagrams, which are similar to traditional isospike diagrams, to display the different periodicities and synchronization properties in the I−G parameter space, where G is the ratio between the Josephson energy and the magnetic anisotropy energy. We find that as I is reduced the onset of chaos occurs shortly before the transition to the superconducting state. This onset of chaos is signaled by a rapid rise in supercurrent (IS⟶I) which corresponds, dynamically, to increasing anharmonicity in phase rotations of the junction.
T2  - Physical Review E
T1  - Chaotic dynamics from coupled magnetic monodomain and Josephson current
VL  - 107
IS  - 2
SP  - 024205
DO  - 10.1103/PhysRevE.107.024205
ER  - 

@article{
author = "Botha, Andre E. and Shukrinov, Yury M. and Tekić, Jasmina and Kolahchi, Mohammad R.",
year = "2023",
abstract = "The ordinary (superconductor-insulator-superconductor) Josephson junction cannot exhibit chaos in the absence of an external ac drive, whereas in the superconductor-ferromagnet-superconductor Josephson junction, known as the φ0 junction, the magnetic layer effectively provides two extra degrees of freedom that can facilitate chaotic dynamics in the resulting four-dimensional autonomous system. In this work, we use the Landau-Lifshitz-Gilbert model for the magnetic moment of the ferromagnetic weak link, while the Josephson junction is described by the resistively capacitively shunted-junction model. We study the chaotic dynamics of the system for parameters surrounding the ferromagnetic resonance region, i.e., for which the Josephson frequency is reasonably close to the ferromagnetic frequency. We show that, due to the conservation of magnetic moment magnitude, two of the numerically computed full spectrum Lyapunov characteristic exponents are trivially zero. One-parameter bifurcation diagrams are used to investigate various transitions that occur between quasiperiodic, chaotic, and regular regions as the dc-bias current through the junction, I, is varied. We also compute two-dimensional bifurcation diagrams, which are similar to traditional isospike diagrams, to display the different periodicities and synchronization properties in the I−G parameter space, where G is the ratio between the Josephson energy and the magnetic anisotropy energy. We find that as I is reduced the onset of chaos occurs shortly before the transition to the superconducting state. This onset of chaos is signaled by a rapid rise in supercurrent (IS⟶I) which corresponds, dynamically, to increasing anharmonicity in phase rotations of the junction.",
journal = "Physical Review E",
title = "Chaotic dynamics from coupled magnetic monodomain and Josephson current",
volume = "107",
number = "2",
pages = "024205",
doi = "10.1103/PhysRevE.107.024205"
}

Botha, A. E., Shukrinov, Y. M., Tekić, J.,& Kolahchi, M. R.. (2023). Chaotic dynamics from coupled magnetic monodomain and Josephson current. in Physical Review E, 107(2), 024205.
https://doi.org/10.1103/PhysRevE.107.024205

Botha AE, Shukrinov YM, Tekić J, Kolahchi MR. Chaotic dynamics from coupled magnetic monodomain and Josephson current. in Physical Review E. 2023;107(2):024205.
doi:10.1103/PhysRevE.107.024205 .

Botha, Andre E., Shukrinov, Yury M., Tekić, Jasmina, Kolahchi, Mohammad R., "Chaotic dynamics from coupled magnetic monodomain and Josephson current" in Physical Review E, 107, no. 2 (2023):024205,
https://doi.org/10.1103/PhysRevE.107.024205 . .

TY  - JOUR
AU  - Botha, André E.
AU  - Shukrinov, Yury M.
AU  - Tekić, Jasmina
PY  - 2022
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10157
AB  - The appearance of chaos along the “charged” resonance circuit branch of the current-voltage characteristics is examined in a model of intrinsic Josephson junctions shunted by resistive, inductive and capacitive circuit elements. Detailed numerical simulations of the electric charge density, current-voltage characteristics and various chaos indicators, such as Lyapunov exponents and Poincaré sections are performed over a wide range of relevant system parameters. In mapping the parameter space, several distinctly different regions are found: some completely regular, while others are dominated by chaos, where the rc-frequency determines the appearance and properties of those regions. At higher values of the rc-frequency chaos appears at first over relatively narrow regions at the lower-current end of the rc-branch. As the rc-frequency is lowered, the chaotic region at the lowered-current end of the rc-branch may becomes wider, depending sensitively on the combination of system parameters. Examination of the metric entropy and maximal Kaplan–Yorke dimension shows that the dimensions of the chaotic attractors associated with the chaos do not plateau, as in the overdamped case, but surprisingly increase indefinitely with the number of junctions, indicating that the system is capable of truly high-dimensional chaos. The onset of the chaos along the rc-branch is found to occur via a two-frequency quasi-periodic route. Our results provided a guide for specific parameter combinations that could minimize the chaos, thereby making certain applications potentially more viable.
T2  - Chaos, Solitons and Fractals
T1  - Chaos along the rc-branch of RLC-shunted intrinsic Josephson junctions
VL  - 156
SP  - 111865
DO  - 10.1016/j.chaos.2022.111865
ER  - 

@article{
author = "Botha, André E. and Shukrinov, Yury M. and Tekić, Jasmina",
year = "2022",
abstract = "The appearance of chaos along the “charged” resonance circuit branch of the current-voltage characteristics is examined in a model of intrinsic Josephson junctions shunted by resistive, inductive and capacitive circuit elements. Detailed numerical simulations of the electric charge density, current-voltage characteristics and various chaos indicators, such as Lyapunov exponents and Poincaré sections are performed over a wide range of relevant system parameters. In mapping the parameter space, several distinctly different regions are found: some completely regular, while others are dominated by chaos, where the rc-frequency determines the appearance and properties of those regions. At higher values of the rc-frequency chaos appears at first over relatively narrow regions at the lower-current end of the rc-branch. As the rc-frequency is lowered, the chaotic region at the lowered-current end of the rc-branch may becomes wider, depending sensitively on the combination of system parameters. Examination of the metric entropy and maximal Kaplan–Yorke dimension shows that the dimensions of the chaotic attractors associated with the chaos do not plateau, as in the overdamped case, but surprisingly increase indefinitely with the number of junctions, indicating that the system is capable of truly high-dimensional chaos. The onset of the chaos along the rc-branch is found to occur via a two-frequency quasi-periodic route. Our results provided a guide for specific parameter combinations that could minimize the chaos, thereby making certain applications potentially more viable.",
journal = "Chaos, Solitons and Fractals",
title = "Chaos along the rc-branch of RLC-shunted intrinsic Josephson junctions",
volume = "156",
pages = "111865",
doi = "10.1016/j.chaos.2022.111865"
}

Botha, A. E., Shukrinov, Y. M.,& Tekić, J.. (2022). Chaos along the rc-branch of RLC-shunted intrinsic Josephson junctions. in Chaos, Solitons and Fractals, 156, 111865.
https://doi.org/10.1016/j.chaos.2022.111865

Botha AE, Shukrinov YM, Tekić J. Chaos along the rc-branch of RLC-shunted intrinsic Josephson junctions. in Chaos, Solitons and Fractals. 2022;156:111865.
doi:10.1016/j.chaos.2022.111865 .

Botha, André E., Shukrinov, Yury M., Tekić, Jasmina, "Chaos along the rc-branch of RLC-shunted intrinsic Josephson junctions" in Chaos, Solitons and Fractals, 156 (2022):111865,
https://doi.org/10.1016/j.chaos.2022.111865 . .

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 . .