Isospectral Transformations
A New Approach to Analyzing Multidimensional Systems and Networks
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Beschreibung
This book presents a new approach to the analysis of networks, which emphasizes how one can compress a network while preserving all information relative to the network's spectrum. This approach can be applied to any network irrespective of the network's structure or whether the network is directed, undirected, weighted, unweighted, etc. Besides these compression techniques, the authors introduce a number of other isospectral transformations and demonstrate how, together, these methods can be applied to gain new results in a number of areas. This includes the stability of time-delayed and non time-delayed dynamical networks, eigenvalue estimation, pseudospectra analysis, and the estimation of survival probabilities in open dynamical systems.
The theory of isospectral transformations, developed in this text, can be readily applied in any area that involves the analysis of multidimensional systems and is especially applicable to the analysis of network dynamics. This book will be of interest to mathematicians, physicists, biologists, engineers and to anyone who has an interest in the dynamics of networks.
This book presents a new approach to the analysis of networks, which emphasizes how one can compress a network while preserving all information relative to the network's spectrum. Besides these compression techniques, the authors introduce a number of other isospectral transformations and demonstrate how, together, these methods can be applied to gain new results in a number of areas. This includes the stability of time-delayed and non time-delayed dynamical networks, eigenvalue estimation, pseudospectra analysis and the estimation of survival probabilities in open dynamical systems. The theory of isospectral transformations, developed in this text, can be readily applied in any area that involves the analysis of multidimensional systems and is especially applicable to the analysis of network dynamics. This book will be of interest to Mathematicians, Physicists, Biologists, Engineers and to anyone who has an interest in the dynamics of networks.
Dynamical networks is a hot topic The first book to highlight the isospectral matrix reduction of networks and put into context of traditional networks literature Static and dynamical properties of networks are covered Includes supplementary material: sn.pub/extras
Autor*in
Leonid Bunimovich
Themen in »Isospectral Transformations«
Estimation of the Spectra of Matrices Isospectral Networks Expansions and Applications Spectrally Equivalent Networks Survival Probabilities dynamical networks isospectral matrix reduction
Stimmen zu »Isospectral Transformations«
“An interesting fact is that a matrix with functional entries can have the same spectrum as a larger matrix with real entries. This is the foundation of the monograph under review. … The monograph is of significance for those specializing in the study of linear algebra applications to dynamical systems, and in particular for graduate students and researchers interested in the stability of dynamical networks.” (Juan Gonzalo Barajas-Ramírez, Mathematical Reviews, June, 2015)
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