TY  - JOUR
AU  - Zdravković, Slobodan
AU  - Zeković, Slobodan
AU  - Bugay, Aleksandr Nikolaevich
AU  - Petrović, Jovana S.
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9918
AB  - In the present work, we study the nonlinear dynamics of microtubules, the basic components of the eukaryotic cytoskeleton. We introduce a two-component model describing tangential oscillations of dimers. A crucial nonlinear differential equation is solved using continuum approximation. We show that the dynamics of microtubules can be explained in terms of kink and antikink solitary waves. We used two mathematical procedures, that is the tangent hyperbolic function method and, more general, the simplest equation method. It is shown that both procedures bring about equal solutions. © 2021
T2  - Chaos, Solitons and Fractals
T1  - Two component model of microtubules and continuum approximation
VL  - 152
SP  - 111352
DO  - 10.1016/j.chaos.2021.111352
ER  - 

@article{
author = "Zdravković, Slobodan and Zeković, Slobodan and Bugay, Aleksandr Nikolaevich and Petrović, Jovana S.",
year = "2021",
abstract = "In the present work, we study the nonlinear dynamics of microtubules, the basic components of the eukaryotic cytoskeleton. We introduce a two-component model describing tangential oscillations of dimers. A crucial nonlinear differential equation is solved using continuum approximation. We show that the dynamics of microtubules can be explained in terms of kink and antikink solitary waves. We used two mathematical procedures, that is the tangent hyperbolic function method and, more general, the simplest equation method. It is shown that both procedures bring about equal solutions. © 2021",
journal = "Chaos, Solitons and Fractals",
title = "Two component model of microtubules and continuum approximation",
volume = "152",
pages = "111352",
doi = "10.1016/j.chaos.2021.111352"
}

Zdravković, S., Zeković, S., Bugay, A. N.,& Petrović, J. S.. (2021). Two component model of microtubules and continuum approximation. in Chaos, Solitons and Fractals, 152, 111352.
https://doi.org/10.1016/j.chaos.2021.111352

Zdravković S, Zeković S, Bugay AN, Petrović JS. Two component model of microtubules and continuum approximation. in Chaos, Solitons and Fractals. 2021;152:111352.
doi:10.1016/j.chaos.2021.111352 .

Zdravković, Slobodan, Zeković, Slobodan, Bugay, Aleksandr Nikolaevich, Petrović, Jovana S., "Two component model of microtubules and continuum approximation" in Chaos, Solitons and Fractals, 152 (2021):111352,
https://doi.org/10.1016/j.chaos.2021.111352 . .

TY  - JOUR
AU  - Zdravković, Slobodan
AU  - Čevizović, Dalibor
AU  - Bugay, Aleksandr N.
AU  - Maluckov, Aleksandra
PY  - 2019
UR  - http://aip.scitation.org/doi/10.1063/1.5090962
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8207
AB  - We study nonlinear dynamics of the DNA molecule relying on a helicoidal Peyrard-Bishop model. We look for traveling wave solutions and show that a continuum approximation brings about kink solitons moving along the chain. This statement is supported by the numerical solution of a relevant dynamical equation of motion. Finally, we argue that an existence of both kinks and localized modulated solitons (breathers) could be a useful tool to describe DNA-RNA transcription. © 2019 Author(s).
T2  - Chaos
T1  - Stationary solitary and kink solutions in the helicoidal Peyrard-Bishop model of DNA molecule
VL  - 29
IS  - 5
SP  - 053118
DO  - 10.1063/1.5090962
ER  - 

@article{
author = "Zdravković, Slobodan and Čevizović, Dalibor and Bugay, Aleksandr N. and Maluckov, Aleksandra",
year = "2019",
abstract = "We study nonlinear dynamics of the DNA molecule relying on a helicoidal Peyrard-Bishop model. We look for traveling wave solutions and show that a continuum approximation brings about kink solitons moving along the chain. This statement is supported by the numerical solution of a relevant dynamical equation of motion. Finally, we argue that an existence of both kinks and localized modulated solitons (breathers) could be a useful tool to describe DNA-RNA transcription. © 2019 Author(s).",
journal = "Chaos",
title = "Stationary solitary and kink solutions in the helicoidal Peyrard-Bishop model of DNA molecule",
volume = "29",
number = "5",
pages = "053118",
doi = "10.1063/1.5090962"
}

Zdravković, S., Čevizović, D., Bugay, A. N.,& Maluckov, A.. (2019). Stationary solitary and kink solutions in the helicoidal Peyrard-Bishop model of DNA molecule. in Chaos, 29(5), 053118.
https://doi.org/10.1063/1.5090962

Zdravković S, Čevizović D, Bugay AN, Maluckov A. Stationary solitary and kink solutions in the helicoidal Peyrard-Bishop model of DNA molecule. in Chaos. 2019;29(5):053118.
doi:10.1063/1.5090962 .

Zdravković, Slobodan, Čevizović, Dalibor, Bugay, Aleksandr N., Maluckov, Aleksandra, "Stationary solitary and kink solutions in the helicoidal Peyrard-Bishop model of DNA molecule" in Chaos, 29, no. 5 (2019):053118,
https://doi.org/10.1063/1.5090962 . .