ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


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: 
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  2. Leonov GA. An estimate for the bifurcation parameters of the saddle separatrix loop of the Lorenz system. Differ. Equ. 1988;24(6):634–638.
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  5. Leonov GA, Reitman V. Attraktoreingrenzung fur nichtlineare systeme. Leipzig: Teubner; 1987.
  6. 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
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