Isospectral Transformations

A New Approach to Analyzing Multidimensional Systems and Networks

Leonid Bunimovich, Benjamin Webb (Autoren)

Buch | Softcover

175 Seiten

2016 | Softcover reprint of the original 1st ed. 2014
Springer-Verlag New York Inc.
978-1-4939-4600-6 (ISBN)

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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.

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.

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.

Erscheinungsdatum	02.10.2016
Reihe/Serie	Springer Monographs in Mathematics
Zusatzinfo	29 Illustrations, color; 22 Illustrations, black and white
Verlagsort	New York
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie
Schlagworte	dynamical networks • Estimation of the Spectra of Matrices • isospectral matrix reduction • Isospectral Networks Expansions and Applications • Spectrally Equivalent Networks • Survival Probabilities
ISBN-10	1-4939-4600-5 / 1493946005
ISBN-13	978-1-4939-4600-6 / 9781493946006
Zustand	Neuware