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Condensed Matter > Disordered Systems and Neural Networks

arXiv:2108.07893 (cond-mat)
[Submitted on 12 Aug 2021 (v1), last revised 24 Jan 2022 (this version, v3)]

Title:Failure of the simultaneous block diagonalization technique applied to complete and cluster synchronization of random networks

Authors:Shirin Panahi, Nelson Amaya, Isaac Klickstein, Galen Novello, Francesco Sorrentino
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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.
Comments: Accepted for publication in PRE
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Systems and Control (eess.SY)
Cite as: arXiv:2108.07893 [cond-mat.dis-nn]
  (or arXiv:2108.07893v3 [cond-mat.dis-nn] for this version)
  https://doi.org/10.48550/arXiv.2108.07893
Related DOI: https://doi.org/10.1103/PhysRevE.105.014313

Submission history

From: Shirin Panahi [view email]
[v1] Thu, 12 Aug 2021 18:27:32 UTC (711 KB)
[v2] Mon, 10 Jan 2022 14:23:21 UTC (2,732 KB)
[v3] Mon, 24 Jan 2022 17:17:25 UTC (2,240 KB)
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