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2014 | Buch

Isospectral Matrix Reductions Kapitel lesen Erstes Kapitel lesen

Isospectral Transformations

A New Approach to Analyzing Multidimensional Systems and Networks

verfasst von: Leonid Bunimovich, Benjamin Webb

Verlag: Springer New York

Buchreihe : Springer Monographs in Mathematics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Isospectral Matrix Reductions
Abstract
This is a fundamental chapter of the book. It deals with networks, which are here considered as graphs, and is built on the theory developed in the previous chapter, on matrices.
Although, the dynamical networks described in Chap. 3 are richer objects than their weighted adjacency matrices, the latter still carry the most important information about a dynamical network. Indeed, from a theoretical point of view, a network’s weighted adjacency matrix describes a linearization of the network’s dynamics, which in applications is often the only network information available. In fact, it is not uncommon to have only the unweighted adjacency matrix of a network.
Leonid Bunimovich, Benjamin Webb
Chapter 2. Dynamical Networks and Isospectral Graph Reductions
Abstract
This is a fundamental chapter of the book. It deals with networks, which are here considered as graphs, and is built on the theory developed in the previous chapter, on matrices.
Although, the dynamical networks described in Chap. 3 are richer objects than their weighted adjacency matrices, the latter still carry the most important information about a dynamical network. Indeed, from a theoretical point of view, a network’s weighted adjacency matrix describes a linearization of the network’s dynamics, which in applications is often the only network information available. In fact, it is not uncommon to have only the unweighted adjacency matrix of a network.
Leonid Bunimovich, Benjamin Webb
Chapter 3. Stability of Dynamical Networks
Abstract
This is a fundamental chapter of the book. It deals with networks, which are here considered as graphs, and is built on the theory developed in the previous chapter, on matrices.
Although, the dynamical networks described in Chap. 3 are richer objects than their weighted adjacency matrices, the latter still carry the most important information about a dynamical network. Indeed, from a theoretical point of view, a network’s weighted adjacency matrix describes a linearization of the network’s dynamics, which in applications is often the only network information available. In fact, it is not uncommon to have only the unweighted adjacency matrix of a network.
Leonid Bunimovich, Benjamin Webb
Chapter 4. Improved Eigenvalue Estimates
Abstract
This is a fundamental chapter of the book. It deals with networks, which are here considered as graphs, and is built on the theory developed in the previous chapter, on matrices.
Although, the dynamical networks described in Chap. 3 are richer objects than their weighted adjacency matrices, the latter still carry the most important information about a dynamical network. Indeed, from a theoretical point of view, a network’s weighted adjacency matrix describes a linearization of the network’s dynamics, which in applications is often the only network information available. In fact, it is not uncommon to have only the unweighted adjacency matrix of a network.
Leonid Bunimovich, Benjamin Webb
Chapter 5. Pseudospectra and Inverse Pseudospectra
Abstract
This is a fundamental chapter of the book. It deals with networks, which are here considered as graphs, and is built on the theory developed in the previous chapter, on matrices.
Although, the dynamical networks described in Chap. 3 are richer objects than their weighted adjacency matrices, the latter still carry the most important information about a dynamical network. Indeed, from a theoretical point of view, a network’s weighted adjacency matrix describes a linearization of the network’s dynamics, which in applications is often the only network information available. In fact, it is not uncommon to have only the unweighted adjacency matrix of a network.
Leonid Bunimovich, Benjamin Webb
Chapter 6. Improved Estimates of Survival Probabilities
Abstract
This is a fundamental chapter of the book. It deals with networks, which are here considered as graphs, and is built on the theory developed in the previous chapter, on matrices.
Although, the dynamical networks described in Chap. 3 are richer objects than their weighted adjacency matrices, the latter still carry the most important information about a dynamical network. Indeed, from a theoretical point of view, a network’s weighted adjacency matrix describes a linearization of the network’s dynamics, which in applications is often the only network information available. In fact, it is not uncommon to have only the unweighted adjacency matrix of a network.
Leonid Bunimovich, Benjamin Webb
Backmatter
Metadaten
Titel
Isospectral Transformations
verfasst von
Leonid Bunimovich
Benjamin Webb
Copyright-Jahr
2014
Verlag
Springer New York
Electronic ISBN
978-1-4939-1375-6
Print ISBN
978-1-4939-1374-9
DOI
https://doi.org/10.1007/978-1-4939-1375-6