Synchronization of dynamical hypernetworks: Dimensionality reduction through simultaneous block-diagonalization of matrices
Year: 2012
Type: article
Abstract: We present a general framework to study stability of the synchronous solution for a hypernetwork of coupled dynamical systems. We are able to reduce the dimensionality of the problem by using simultaneous block diagonalization of matrices. We obtain necessary and sufficient conditions for stability of the synchronous solution in terms of a set of lower-dimensional problems and test the predictions of our low-dimensional analysis through numerical simulations. Under certain conditions, this technique may yield a substantial reduction of the dimensionality of the problem. For example, for a class of dynamical hypernetworks analyzed in the paper, we discover that arbitrarily large networks can be reduced to a collection of subsystems of dimensionality no more than 2. We apply our reduction technique to a number of different examples, including the class of undirected unweighted hypermotifs with 3 nodes.
Source: Physical Review E
Authors: Daniel Irving, Francesco Sorrentino
Institution: University of New Mexico
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1993230952