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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

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