Isospectral Transformations

A New Approach to Analyzing Multidimensional Systems and Networks

  • Leonid Bunimovich
  • Benjamin Webb
Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Leonid Bunimovich, Benjamin Webb
    Pages 1-17
  3. Leonid Bunimovich, Benjamin Webb
    Pages 19-52
  4. Leonid Bunimovich, Benjamin Webb
    Pages 53-89
  5. Leonid Bunimovich, Benjamin Webb
    Pages 91-127
  6. Leonid Bunimovich, Benjamin Webb
    Pages 129-146
  7. Leonid Bunimovich, Benjamin Webb
    Pages 147-170
  8. Back Matter
    Pages 171-175

About this book

Introduction

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.

Keywords

Estimation of the Spectra of Matrices Isospectral Networks Expansions and Applications Spectrally Equivalent Networks Survival Probabilities dynamical networks isospectral matrix reduction

Authors and affiliations

  • Leonid Bunimovich
    • 1
  • Benjamin Webb
    • 2
  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of Mathematics,Brigham Young UniversityProvoUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-1375-6
  • Copyright Information Springer Science+Business Media New York 2014
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-1374-9
  • Online ISBN 978-1-4939-1375-6
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • About this book