Isospectral Graph Transformations, Spectral Equivalence, and Global Stability of Dynamical Networks

Autor:	Bunimovich, L. A., Webb, B. Z.
Rok vydání:	2010
Předmět:	Mathematics - Dynamical Systems Nonlinear Sciences - Chaotic Dynamics 05C50 15A18 37C75
Druh dokumentu:	Working Paper
Popis:	In this paper we present a general procedure that allows for the reduction or expansion of any network (considered as a weighted graph). This procedure maintains the spectrum of the network's adjacency matrix up to a set of eigenvalues known beforehand from its graph structure. This procedure can be used to establish new equivalence relations on the class of all weighted graphs (networks) where two graphs are equivalent if they can be reduced to the same graph. Additionally, dynamical networks (or any finite dimensional, discrete time dynamical system) can be analyzed using isospectral transformations. By so doing we obtain stronger results regarding the global stability (strong synchronization) of dynamical networks when compared to other standard methods. Comment: Contains extensions of some results from the previous Arxiv submission "Isospectral Graph Reductions"
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1010.3272 Zobrazit plný text záznamu View this record from Arxiv