English

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