The principle of symmetry in three-dimensional systems

ЗаголовокThe principle of symmetry in three-dimensional systems
Тип публікаціїJournal Article
Рік публікації2017
АвториNikitina, NV
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2017.07.021
Номер видання7
РозділMechanics
Нумерація сторінок21-28
Дата публікації7/2017
МоваRussian
Анотація

The application of the principle of symmetry (skew symmetry) in three-dimensional nonlinear systems is analyzed. The development of the principle is associated with the establishment of the existence of an attractor and a certain symmetry of its projections on the coordinate planes.
Ключові словаbifurcation, symmetry principles, three-dimensional nonlinear system
Посилання: 
  1. Nemytskii, V. V. and Stepanov, V. V. (1960). Qualitative Theory of Differential Equation. Princeton: Princeton Univ. Press.
  2. Nikitina, N. V. (2012). Nonlinear systems with complex and chaotic behavior of traectories. Kyiv: Phenix (in Russian).
  3. Anishechenro, V. S., Astakhov, V. V., Vadivasova, T. E., Sosnovtseva, O. V., Wu, C. W., Chua, L. (1995). Dynamics of two coupled Chua's curchuits. Int. J. Bifurcation and Chaos, 5, No. 6, pp. 1677-1699. https://doi.org/10.1142/S0218127495001241
  4. Shilnikov, L. P., Shilnikov, A. L., Turaev, D. V., Chua, L. O. (2001). Methods of Qualitative Theory in Nonlinear Dynamics. Part II. Singapore: World Scientific. https://doi.org/10.1142/4221
  5. Anishchenko, V. S. (1990). Complex Oschillations in Simple Systems. Nauka: Moscow (in Russian).
  6. Martynyuk, A. A., Nikitina, N. V. (2015). Bifurcations and Multi-Stabilty of Vibrations of Three-Dimensional System. Int.Appl.Mech. 51, No. 2, pp. 540-541. https://doi.org/10.1007/s10778-015-0687-5
  7. Martynyuk, A. A., Nikitina, N. V. (2015). On Periodical Motions in Three-Dimensional Systems. Int. Appl. Mech. 51, No. 4, pp. 369-379. https://doi.org/10.1007/s10778-015-0697-3