Failure of the simultaneous block diagonalization technique applied to complete and cluster synchronization of random networks
Disordered Systems and Neural Networks
2022-02-02 v3 Systems and Control
Systems and Control
Abstract
We discuss here the application of the simultaneous block diagonalization (SBD) of matrices to the study of the stability of both complete and cluster synchronization in random (generic) networks. For both problems, we define indices that measure success (or failure) of application of the SBD technique in decoupling the stability problem into problems of lower dimensionality. We then see that in the case of random networks the extent of the dimensionality reduction achievable is the same as that produced by application of a trivial transformation.
Keywords
Cite
@article{arxiv.2108.07893,
title = {Failure of the simultaneous block diagonalization technique applied to complete and cluster synchronization of random networks},
author = {Shirin Panahi and Nelson Amaya and Isaac Klickstein and Galen Novello and Francesco Sorrentino},
journal= {arXiv preprint arXiv:2108.07893},
year = {2022}
}
Comments
Accepted for publication in PRE