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Isospectral Transformations

A New Approach to Analyzing Multidimensional Systems and Networks

  • Book
  • © 2014

Overview

Authors:
  1. Leonid Bunimovich

    1. School of Mathematics, Georgia Institute of Technology, Atlanta, USA

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  2. Benjamin Webb

    1. Department of Mathematics,, Brigham Young University, Provo, USA

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    You can also search for this author in PubMed   Google Scholar

  • 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

Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Isospectral Matrix Reductions

    • Leonid Bunimovich, Benjamin Webb
    Pages 1-17

  3. Dynamical Networks and Isospectral Graph Reductions

    • Leonid Bunimovich, Benjamin Webb
    Pages 19-52

  4. Stability of Dynamical Networks

    • Leonid Bunimovich, Benjamin Webb
    Pages 53-89

  5. Improved Eigenvalue Estimates

    • Leonid Bunimovich, Benjamin Webb
    Pages 91-127

  6. Pseudospectra and Inverse Pseudospectra

    • Leonid Bunimovich, Benjamin Webb
    Pages 129-146

  7. Improved Estimates of Survival Probabilities

    • Leonid Bunimovich, Benjamin Webb
    Pages 147-170

  8. Back Matter

    Pages 171-175
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Keywords

About this book

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.

Reviews

“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)

Authors and Affiliations

  • School of Mathematics, Georgia Institute of Technology, Atlanta, USA

    Leonid Bunimovich

  • Department of Mathematics,, Brigham Young University, Provo, USA

    Benjamin Webb

About the authors

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.

Bibliographic Information

  • Book Title: Isospectral Transformations

  • Book Subtitle: A New Approach to Analyzing Multidimensional Systems and Networks

  • Authors: Leonid Bunimovich, Benjamin Webb

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4939-1375-6

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media New York 2014

  • Hardcover ISBN: 978-1-4939-1374-9Published: 03 September 2014

  • Softcover ISBN: 978-1-4939-4600-6Published: 17 September 2016

  • eBook ISBN: 978-1-4939-1375-6Published: 03 September 2014

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XVI, 175

  • Number of Illustrations: 22 b/w illustrations, 29 illustrations in colour

  • Topics: Dynamical Systems and Ergodic Theory, Mathematical Methods in Physics, Complex Systems

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