Multiparameter bifurcation and stability of solutions at a double eigenvalue

This paper deals with some problems of bifurcation theory for general non-linear eigenvalue prob-lem for 2-dimensional parameter space. An explicit analysis of the bifurcation for 2-dimensional parameter space is done and the structure of the non-trivial solution branches of the bifurcation equation...

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1. Verfasser:	Bari, Rehana
Format:	Artikel
Sprache:	English
Veröffentlicht:	BRAC University 2010
Schlagworte:	Non-linear eigenvalue problem Bifurcating solutions Linearised operator Lyapunov-Schmidt method Stability
Online Zugang:	http://hdl.handle.net/10361/521

id	10361-521
record_format	dspace
spelling	10361-5212019-09-29T05:46:00Z Multiparameter bifurcation and stability of solutions at a double eigenvalue Bari, Rehana Non-linear eigenvalue problem Bifurcating solutions Linearised operator Lyapunov-Schmidt method Stability This paper deals with some problems of bifurcation theory for general non-linear eigenvalue prob-lem for 2-dimensional parameter space. An explicit analysis of the bifurcation for 2-dimensional parameter space is done and the structure of the non-trivial solution branches of the bifurcation equation near origin is given. Since the study of the bifurcation problem is closely related to change in the qualitative behaviour of the systems, and to exchange of stability, analysis of the stability of the bifurcating solutions is done here. It is proved that the stability of the bifurcating solutions is de-termined, to the lowest non-vanishing order, by the eigenvalues of the Fréchet derivative of the re-duced bifurcation equation. 2010-10-14T10:25:53Z 2010-10-14T10:25:53Z 2004 Article http://hdl.handle.net/10361/521 en BRAC University Journal, BRAC University;Vol.1, No.2,pp. 115-122 application/pdf BRAC University
institution	Brac University
collection	Institutional Repository
language	English
topic	Non-linear eigenvalue problem Bifurcating solutions Linearised operator Lyapunov-Schmidt method Stability
spellingShingle	Non-linear eigenvalue problem Bifurcating solutions Linearised operator Lyapunov-Schmidt method Stability Bari, Rehana Multiparameter bifurcation and stability of solutions at a double eigenvalue
description	This paper deals with some problems of bifurcation theory for general non-linear eigenvalue prob-lem for 2-dimensional parameter space. An explicit analysis of the bifurcation for 2-dimensional parameter space is done and the structure of the non-trivial solution branches of the bifurcation equation near origin is given. Since the study of the bifurcation problem is closely related to change in the qualitative behaviour of the systems, and to exchange of stability, analysis of the stability of the bifurcating solutions is done here. It is proved that the stability of the bifurcating solutions is de-termined, to the lowest non-vanishing order, by the eigenvalues of the Fréchet derivative of the re-duced bifurcation equation.
format	Article
author	Bari, Rehana
author_facet	Bari, Rehana
author_sort	Bari, Rehana
title	Multiparameter bifurcation and stability of solutions at a double eigenvalue
title_short	Multiparameter bifurcation and stability of solutions at a double eigenvalue
title_full	Multiparameter bifurcation and stability of solutions at a double eigenvalue
title_fullStr	Multiparameter bifurcation and stability of solutions at a double eigenvalue
title_full_unstemmed	Multiparameter bifurcation and stability of solutions at a double eigenvalue
title_sort	multiparameter bifurcation and stability of solutions at a double eigenvalue
publisher	BRAC University
publishDate	2010
url	http://hdl.handle.net/10361/521
work_keys_str_mv	AT barirehana multiparameterbifurcationandstabilityofsolutionsatadoubleeigenvalue
_version_	1814309089129267200

Multiparameter bifurcation and stability of solutions at a double eigenvalue

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