About the existence of a homoclinic trajectory with symmetry in the three-dimensional systems
DOI:
https://doi.org/10.15407/dopovidi2014.07.068Keywords:
homoclinic trajectory, symmetry, three-dimensional systemsAbstract
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.
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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).
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).
Andronov A. A., Vitt A. A., Khaikin C. E. Theory of oscillations. Moscow: Nauka, 1981 (in Russian).
Anishchenko V. S. Complex oscillations in simple systems. Moscow: Nauka, 1990 (in Russian).
Neimark Yu. I., Landa P. S. Stochastic and chaotic oscillations. Moscow: Nauka, 1987 (in Russian).
Belhaq M., Lakrad F. Intern. J. of Bifurcation and Chaos., 2002, 12, No. 11: 2479–2486. https://doi.org/10.1142/S0218127402005996
Leonov G. A. Strange attractors and classical stability theory. St.-Peterburg: Univ. Press, 2008.
Leonov G. A. Prikl. mekh. i mat., 2013, 77, Iss. 3: 410–421 (in Russian).
Nikitina N. V. Nonlinear systems with complex and chaotic behavior of trajectories. Kyiv: Feniks, 2012 (in Russian).
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).
Gurina T. A., Dorofeev I. A. Dinamich. sistemy, 2010, 77, Iss. 28: 63–68 (in Russian).
Nemytskyi V. V., Stepanov V. V. Qualitative theory of differential equations. Moscow; Leningrad: Gostekhteorizdat, 1949 (in Russian).
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