Details

Isospectral Transformations

A New Approach to Analyzing Multidimensional Systems and Networks
Springer Monographs in Mathematics

von: Leonid Bunimovich, Benjamin Webb
53,49 €
Verlag:	Springer
Format:	PDF
Veröffentl.:	03.09.2014
ISBN/EAN:	9781493913756
Sprache:	englisch

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Beschreibungen

Titelbeschreibung

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

Isospectral Transformations: A New Approach to Analyzing Multidimensional Systems and Networks.- Isospectral Matrix Reductions.- Dynamical Networks and Isospectral Graph Reductions.- Stability of Dynamical Networks.- Improved Eigenvalue Estimates.- Pseudospectra and Inverse Pseudospectra.- Improved Estimates of Survival Probabilities.

Autorenportrait

Leonid Bunimovich is a Professor of Mathematics and Director of the ABC Math Program at Georgia Institute of Technology. Professor Bunimovich's fields of interest include: Dynamical Systems, Ergodic Theory, Statistical Mechanics, Space-Time Chaos, Intermittency and Coherent Structures in Extended Systems, Geophysical Hydrodynamics, Mathematical Biology, Quantum Chaos, Waves in Nonhomogeneous Media, Lattice Gases, Cellular Automata, Percolation, Limit Theorems for Chaotic Dynamical Systems, Neuroscience, Operations Research.Benjamin Webb is currently a visiting Assistant Professor in the Department of Mathematics at Brigham Young University. He has earned his PhD in Mathematics at the Georgia Institute of Technology.

Back cover copy

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.

Sonderbeitrag

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