Synchronized Hopf Bifurcation Analysis in a Delay-Coupled Semiconductor Lasers System

Synchronized Hopf Bifurcation Analysis in a Delay-Coupled Semiconductor Lasers System

The dynamics of a system of two semiconductor lasers, which are delay coupled via a passive relay within the synchronization manifold, are investigated. Depending on the coupling parameters, the system exhibits synchronized Hopf bifurcation and the stability switches as the delay varies. Employing t...

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Main Authors: Gang Zhu, Junjie Wei
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/257635
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spelling doaj-b2ca91205c894ef7b247f915727f3a692020-11-24T20:58:38ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/257635257635Synchronized Hopf Bifurcation Analysis in a Delay-Coupled Semiconductor Lasers SystemGang Zhu0Junjie Wei1Department of Mathematics, Harbin Institute of Technology, Heilongjiang, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Heilongjiang, Harbin 150001, ChinaThe dynamics of a system of two semiconductor lasers, which are delay coupled via a passive relay within the synchronization manifold, are investigated. Depending on the coupling parameters, the system exhibits synchronized Hopf bifurcation and the stability switches as the delay varies. Employing the center manifold theorem and normal form method, an algorithm is derived for determining the Hopf bifurcation properties. Some numerical simulations are carried out to illustrate the analysis results.http://dx.doi.org/10.1155/2012/257635
collection DOAJ
language English
format Article
sources DOAJ
author Gang Zhu
Junjie Wei
spellingShingle Gang Zhu
Junjie Wei
Synchronized Hopf Bifurcation Analysis in a Delay-Coupled Semiconductor Lasers System
Journal of Applied Mathematics
author_facet Gang Zhu
Junjie Wei
author_sort Gang Zhu
title Synchronized Hopf Bifurcation Analysis in a Delay-Coupled Semiconductor Lasers System
title_short Synchronized Hopf Bifurcation Analysis in a Delay-Coupled Semiconductor Lasers System
title_full Synchronized Hopf Bifurcation Analysis in a Delay-Coupled Semiconductor Lasers System
title_fullStr Synchronized Hopf Bifurcation Analysis in a Delay-Coupled Semiconductor Lasers System
title_full_unstemmed Synchronized Hopf Bifurcation Analysis in a Delay-Coupled Semiconductor Lasers System
title_sort synchronized hopf bifurcation analysis in a delay-coupled semiconductor lasers system
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
description The dynamics of a system of two semiconductor lasers, which are delay coupled via a passive relay within the synchronization manifold, are investigated. Depending on the coupling parameters, the system exhibits synchronized Hopf bifurcation and the stability switches as the delay varies. Employing the center manifold theorem and normal form method, an algorithm is derived for determining the Hopf bifurcation properties. Some numerical simulations are carried out to illustrate the analysis results.
url http://dx.doi.org/10.1155/2012/257635
work_keys_str_mv AT gangzhu synchronizedhopfbifurcationanalysisinadelaycoupledsemiconductorlaserssystem
AT junjiewei synchronizedhopfbifurcationanalysisinadelaycoupledsemiconductorlaserssystem
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