Title | About the existence of a homoclinic trajectory with symmetry in the three-dimensional systems |
Publication Type | Journal Article |
Year of Publication | 2014 |
Authors | Nikitina, NV |
Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
DOI | 10.15407/dopovidi2014.07.068 |
Issue | 7 |
Section | Mechanics |
Pagination | 68-75 |
Date Published | 7/2014 |
Language | Russian |
Abstract | The conditions of existence of a homoclinic trajectory are obtained for a system set in the three-dimensional space. The dissipative system with symmetry is considered. |
Keywords | homoclinic trajectory, symmetry, three-dimensional systems |
1. Shilnikov L. P., Shilnikov A. L., Turaev D. V., Chua L. Methods of the qualitative theory in nonlinear dynamics. Pt. 1. Moscow; Izhevsk: IKI, 2004 (in Russian).
2. Shilnikov L. P., Shilnikov A. L., Turaev D. V., Chua L. Methods of the qualitative theory in nonlinear dynamics. Pt. 2. Moscow; Izhevsk: IKI, 2009 (in Russian).
3. Andronov A. A., Vitt A. A., Khaikin C. E. Theory of oscillations. Moscow: Nauka, 1981 (in Russian).
4. Anishchenko V. S. Complex oscillations in simple systems. Moscow: Nauka, 1990 (in Russian).
5. Neimark Yu. I., Landa P. S. Stochastic and chaotic oscillations. Moscow: Nauka, 1987 (in Russian).
6. Belhaq M., Lakrad F. Intern. J. of Bifurcation and Chaos., 2002, 12, No. 11: 2479–2486. https://doi.org/10.1142/S0218127402005996
7. Leonov G. A. Strange attractors and classical stability theory. St.-Peterburg: Univ. Press, 2008.
8. Leonov G. A. Prikl. mekh. i mat., 2013, 77, Iss. 3: 410–421 (in Russian).
9. Nikitina N. V. Nonlinear systems with complex and chaotic behavior of trajectories. Kyiv: Feniks, 2012 (in Russian).
10. Shapovalov V. I., Kablov V. F., Bashmakov V. A., Avakumov V. E. Synergetic model of stability of an average firm. In: Kolesnikov A. A. (Ed.) Synergetics and problems of control theory. Moscow: Fizmatlit, 2004: 454–464 (in Russian).
11. Gurina T. A., Dorofeev I. A. Dinamich. sistemy, 2010, 77, Iss. 28: 63–68 (in Russian).
12. Nemytskyi V. V., Stepanov V. V. Qualitative theory of differential equations. Moscow; Leningrad: Gostekhteorizdat, 1949 (in Russian).