Isospectral Transformations A New Approach to Analyzing Multidimensional Systems and Networks - Bunimovich, Leonid; Webb, Benjamin; SpringerLink (Online service) (New York, NY : Springer New York : Imprint: Springer, 2014)
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.
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.
Keywords: Mathematics; Dynamics; Ergodic theory; System theory; Physics; Mathematics; Dynamical Systems and Ergodic Theory; Mathematical Methods in Physics; Complex Systems; Electronic books