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Proceedings Paper

Homoclinic codimension-2 points and three-level laser models
Author(s): Andrey L. Shil'nikov
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Paper Abstract

A description of the principal bifurcations which lead to the appearance of the Lorenz attractor is given for the 3D normal form for codimension-3 bifurcations of equilibria and periodic orbits in systems with symmetry. We pay special attention to two bifurcation points corresponding to the formation of a homoclinic butterfly of a saddle with unit saddle index and to a homoclinic butterfly with zero separatrix value.

Paper Details

Date Published: 6 July 1994
PDF: 8 pages
Proc. SPIE 2099, Nonlinear Dynamics in Lasers and Optical Systems, (6 July 1994); doi: 10.1117/12.179641
Show Author Affiliations
Andrey L. Shil'nikov, Research Institute for Applied Mathematics and Cybernetics (Russia)


Published in SPIE Proceedings Vol. 2099:
Nonlinear Dynamics in Lasers and Optical Systems
Neal Broadus Abraham; Leonid A. Melnikov; Anatoly N. Oraevsky; Yakov I. Khanin, Editor(s)

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