Panahi Shirin, Amaya Nelson, Klickstein Isaac, Novello Galen, Sorrentino Francesco
University of New Mexico, Albuquerque, New Mexico 80131, USA.
Phys Rev E. 2022 Jan;105(1-1):014313. doi: 10.1103/PhysRevE.105.014313.
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.
