Geodesic
Mathematical modeling of nonlocal oscillatory Duffing system with fractal friction
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 1 (2015), pp. 18-24 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper considers a nonlinear fractal oscillatory Duffing system with friction. The numerical analysis of this system by a finite-difference scheme was carried out. Phase portraits and system solutions were constructed depending on fractional parameters
Keywords: Gerasimov-Caputo operator, Duffing oscillator, finite-difference scheme.
Mots-clés : phase portrait 
@article{VKAM_2015_1_a2,
     author = {R. I. Parovik},
     title = {Mathematical modeling of nonlocal oscillatory {Duffing} system with fractal friction},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {18--24},
     year = {2015},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2015_1_a2/}
}
TY  - JOUR
AU  - R. I. Parovik
TI  - Mathematical modeling of nonlocal oscillatory Duffing system with fractal friction
JO  - Vestnik KRAUNC. Fiziko-matematičeskie nauki
PY  - 2015
SP  - 18
EP  - 24
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VKAM_2015_1_a2/
LA  - ru
ID  - VKAM_2015_1_a2
ER  - 
%0 Journal Article
%A R. I. Parovik
%T Mathematical modeling of nonlocal oscillatory Duffing system with fractal friction
%J Vestnik KRAUNC. Fiziko-matematičeskie nauki
%D 2015
%P 18-24
%N 1
%U http://geodesic.mathdoc.fr/item/VKAM_2015_1_a2/
%G ru
%F VKAM_2015_1_a2
R. I. Parovik. Mathematical modeling of nonlocal oscillatory Duffing system with fractal friction. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 1 (2015), pp. 18-24. http://geodesic.mathdoc.fr/item/VKAM_2015_1_a2/

[1] S. Sh. Rekhviashvili, Razmernye yavleniya v fizike kondensirovannogo sostoyaniya i nanotekhnologiyakh, KBNTs RAN, Nalchik, 2014, 250 pp.

[2] I. Petras, Fractional-Order Nonlinear Systems. Modeling, Analysis and Simulation, Springer, Beijing; Springer-Verlag, Berlin–Heidelberg, 2011, 218 pp. | Zbl

[3] B. G. Kao, “A three-dimensional dynamic tire model for vehicle dynamic simulations”, Tire Science and Technology, 28:2 (2000), 72–95 | DOI

[4] Y. A. Rossikhin, M. V. Shitikova, “Application of fractional calculus for dynamic problems of solid mechanics: novel trends and recent results”, Applied Mechanics Reviews, 63:1 (2010), 010801 | DOI

[5] Syta A., Litak G., Lenci S., Scheffler M., “Chaotic vibrations of the duffing system with fractional damping”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 24:1 (2014), 013107 | DOI | MR

[6] L. J. Sheu, H. K. Chen, J. H .Chen, L. M. Tam, “Chaotic dynamics of the fractionally damped Duffing equation”, Chaos, Solitons Fractals, 32:4 (2007), 1459–1468 | DOI | MR | Zbl

[7] A. M. Nakhushev, Drobnoe ischislenie i ego primenenie, Fizmatlit, M., 2003, 272 pp.

[8] R. I. Parovik, “Chislennyi analiz nekotorykh ostsillyatsionnykh uravnenii s proizvodnoi drobnogo poryadka”, Vestnik KRAUNTs. Fiziko-matematicheskie nauki, 9:2 (2014), 30–35

[9] V. Ebeling, Obrazovanie struktur pri neobratimykh protsessakh. Vvedenie v teoriyu dissipativnykh struktur, Mir, M., 1979, 279 pp.

[10] V. T. Grinchenko, A. A. Snarskii, V. T. Matsypura, Vvedenie v nelineinuyu dinamiku: Khaos i fraktaly, LKI, M., 2007, 264 pp.