Šil'nikov-saddle-node interaction near a codimension-2 bifurcation: Laser with injected signal

We describe a Šil'nikov-saddle-node interaction in the proximity of a Hopf-saddle-node bifurcation both from numerical and theoretical viewpoints, inspired by numerical observations on a three-dimensional model of a laser with injected signal. We describe the interaction near the codimension-2...

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Autores principales: Zimmermann, Martín G., Natiello, Mario Alberto, Solari, Hernán Gustavo
Publicado: 1997
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01672789_v109_n3-4_p293_Zimmermann
http://hdl.handle.net/20.500.12110/paper_01672789_v109_n3-4_p293_Zimmermann
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_01672789_v109_n3-4_p293_Zimmermann
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spelling paper:paper_01672789_v109_n3-4_p293_Zimmermann2023-06-08T15:16:15Z Šil'nikov-saddle-node interaction near a codimension-2 bifurcation: Laser with injected signal Zimmermann, Martín G. Natiello, Mario Alberto Solari, Hernán Gustavo We describe a Šil'nikov-saddle-node interaction in the proximity of a Hopf-saddle-node bifurcation both from numerical and theoretical viewpoints, inspired by numerical observations on a three-dimensional model of a laser with injected signal. We describe the interaction near the codimension-2 point using a return map controlled by the parameters of the bifurcation. The theoretical predictions compare well with numerical experiments. Finally, we discuss the reasons for the existence of the Šil'nikov-saddle-node bifurcation in the laser with injected signal, and correspondingly, the characteristics of other systems that might display this bifurcation. Copyright © 1997 Elsevier Science B.V. All rights reserved. Fil:Zimmermann, M.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Natiello, M.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Solari, H.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 1997 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01672789_v109_n3-4_p293_Zimmermann http://hdl.handle.net/20.500.12110/paper_01672789_v109_n3-4_p293_Zimmermann
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description We describe a Šil'nikov-saddle-node interaction in the proximity of a Hopf-saddle-node bifurcation both from numerical and theoretical viewpoints, inspired by numerical observations on a three-dimensional model of a laser with injected signal. We describe the interaction near the codimension-2 point using a return map controlled by the parameters of the bifurcation. The theoretical predictions compare well with numerical experiments. Finally, we discuss the reasons for the existence of the Šil'nikov-saddle-node bifurcation in the laser with injected signal, and correspondingly, the characteristics of other systems that might display this bifurcation. Copyright © 1997 Elsevier Science B.V. All rights reserved.
author Zimmermann, Martín G.
Natiello, Mario Alberto
Solari, Hernán Gustavo
spellingShingle Zimmermann, Martín G.
Natiello, Mario Alberto
Solari, Hernán Gustavo
Šil'nikov-saddle-node interaction near a codimension-2 bifurcation: Laser with injected signal
author_facet Zimmermann, Martín G.
Natiello, Mario Alberto
Solari, Hernán Gustavo
author_sort Zimmermann, Martín G.
title Šil'nikov-saddle-node interaction near a codimension-2 bifurcation: Laser with injected signal
title_short Šil'nikov-saddle-node interaction near a codimension-2 bifurcation: Laser with injected signal
title_full Šil'nikov-saddle-node interaction near a codimension-2 bifurcation: Laser with injected signal
title_fullStr Šil'nikov-saddle-node interaction near a codimension-2 bifurcation: Laser with injected signal
title_full_unstemmed Šil'nikov-saddle-node interaction near a codimension-2 bifurcation: Laser with injected signal
title_sort šil'nikov-saddle-node interaction near a codimension-2 bifurcation: laser with injected signal
publishDate 1997
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01672789_v109_n3-4_p293_Zimmermann
http://hdl.handle.net/20.500.12110/paper_01672789_v109_n3-4_p293_Zimmermann
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AT natiellomarioalberto silnikovsaddlenodeinteractionnearacodimension2bifurcationlaserwithinjectedsignal
AT solarihernangustavo silnikovsaddlenodeinteractionnearacodimension2bifurcationlaserwithinjectedsignal
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