Treffer: Isospectral graph transformations, spectral equivalence, and global stability of dynamical networks

Title:
Isospectral graph transformations, spectral equivalence, and global stability of dynamical networks
Authors:
BUNIMOVICH, L. A, WEBB, B. Z
Source:
Nonlinearity (Bristol. Print). 25(1):211-254
Publisher Information:
Bristol: Institute of Physics, 2012.
Publication Year:
2012
Physical Description:
print, 28 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Théorie des opérateurs, Operator theory, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Algèbre linéaire numérique, Numerical linear algebra, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Analyse non linéaire, Nonlinear analysis, análisis no lineal, Classe équivalence, Equivalence classes, Expansion, Expansión, Graphe pondéré, Weighted graph, Grafo pondero, Matrice S, S matrix, Matriz S, Matrice adjacence, Adjacency matrix, Matriz adyacencia, Norme, Standards, Norma, Physique mathématique, Mathematical physics, Física matemática, Relation équivalence, Equivalence relation, Relación equivalencia, Stabilité spectrale, Spectral stability, Estabilidad espectral, Synchronisation, Synchronization, Sincronización, Système temps discret, Discrete time systems, Valeur propre, Eigenvalue, Valor propio, 47A10, 65F15, 65H17, Développement mathématique, Mathematical expansion, Stabilité forte, Stabilité globale, Système fini
Document Type:
Fachzeitschrift Article
File Description:
text
Language:
English
Author Affiliations:
ABC Math Program and School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA 30332, United States
Brigham Young University, Department of Mathematics, Provo, UT 84602, United States
ISSN:
0951-7715
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=25413661
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics

Theoretical physics
Accession Number:
edscal.25413661
Database:
PASCAL Archive

Weitere Informationen

In this paper we present a general procedure that allows for the reduction or expansion of any network (considered as a weighted graph). This procedure maintains the spectrum of the network's adjacency matrix up to a set of eigenvalues known beforehand from its graph structure. This procedure can be used to establish new equivalence relations on the class of all weighted graphs (networks) where two graphs are equivalent if they can be reduced to the same graph. Additionally, dynamical networks (or any finite dimensional, discrete time dynamical system) can be analysed using isospectral transformations. By doing so we obtain stronger results regarding the global stability (strong synchronization) of dynamical networks when compared with other standard methods.