Application of largest Lyapunov exponent analysis on the studies of dynamics under external forces
Samo za registrovane korisnike
2017
Članak u časopisu (Objavljena verzija)
![](/themes/MirageVinar//images/creativecommons/arr.png)
Metapodaci
Prikaz svih podataka o dokumentuApstrakt
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 ampli...tude 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.
Ključne reči:
Frenkel-Kontorova model / Josephson junctions arrays / Lyapunov analysis / Incommensurate structuresIzvor:
Communications in Nonlinear Science and Numerical Simulation, 2017, 47, 100-108Finansiranje / projekti:
- Uticaj elementarnih ekscitacija i konformacija na fizička svojstva novih materijala baziranih na jako korelisanim niskodimenzionalnim sistemima (RS-MESTD-Basic Research (BR or ON)-171009)
- Fotonika mikro i nano strukturnih materijala (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-45010)
- Provincial Secretariat for High Education and Scientific Research of Vojvodina [APV 114-451-2201]
Napomena:
- Preprint available at: https://arxiv.org/pdf/1510.07267.pdf
DOI: 10.1016/j.cnsns.2016.11.010
ISSN: 1007-5704; 1878-7274
WoS: 000393247200008
Scopus: 2-s2.0-84998880969
Kolekcije
Institucija/grupa
VinčaTY - 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 . .