For citation:
Ljashko S. A. Sufficient conditions of the Lorenz-system homoclinic orbit existence. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 1, pp. 75-86. DOI: 10.18500/0869-6632-2007-15-1-75-86
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Russian
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Article
UDC:
531.36
Sufficient conditions of the Lorenz-system homoclinic orbit existence
Autors:
Ljashko Sergej Andreevich, Balashov branch of the Saratov State University. N.G. Chernyshevsky
Abstract:
The property of unstable manifold of the Lorenz-system zero equilibrium is proved. This permited to prove the sufficient condition of homoclinic orbit existence.
Key words:
Reference:
- Leonov GA. Bounds for attractors and the existence of homoclinic orbits in the lorenz system. Journal of Applied Mathematics and Mechanics. 2001;65(1):19–32. DOI: 10.1016/S0021-8928(01)00004-1.
- Leonov GA. An estimate for the bifurcation parameters of the saddle separatrix loop of the Lorenz system. Differ. Equ. 1988;24(6):634–638.
- Leonov GA. On estimates of the bifurcation values of the parameters of a Lorentz system. Russian Math. Surveys.1988;43(3):216–217.
- Leonov GA. Effective criteria for the existence of homoclinic bifurcations in dissipative systems. Izvestiya VUZ. Applied Nonlinear Dynamics. 2005;13(3):20–26 (in Russian). DOI: 10.18500/0869-6632-2005-13-3-20-26.
- Leonov GA, Reitman V. Attraktoreingrenzung fur nichtlineare systeme. Leipzig: Teubner; 1987.
- Leonov GA. On homoclinic trajectories in the Lorentz system. Vestn. SPb. Univ. Mat. Mekh. Astron. 1999;1:13–20.
Received:
29.05.2006
Accepted:
29.05.2006
Published:
28.02.2007
Journal issue:
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