scholarly journals Cluster synchronization of networks via a canonical transformation for simultaneous block diagonalization of matrices

2021 ◽  
Vol 31 (11) ◽  
pp. 111102
Author(s):  
Shirin Panahi ◽  
Isaac Klickstein ◽  
Francesco Sorrentino
Keyword(s):  
Canonical Transformation ◽  
Cluster Synchronization ◽  
Block Diagonalization

scholarly journals Unified treatment of synchronization patterns in generalized networks with higher-order, multilayer, and temporal interactions

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Yuanzhao Zhang ◽  
Vito Latora ◽  
Adilson E. Motter
Keyword(s):  
Higher Order ◽  
Cluster Synchronization ◽  
Block Diagonalization ◽  
Unified Framework ◽  
Emergent Phenomena ◽  
Wide Range ◽  
Generalized Networks ◽  
The Stability ◽  
Temporal Interactions ◽  
Synchronization Pattern

AbstractWhen describing complex interconnected systems, one often has to go beyond the standard network description to account for generalized interactions. Here, we establish a unified framework to simplify the stability analysis of cluster synchronization patterns for a wide range of generalized networks, including hypergraphs, multilayer networks, and temporal networks. The framework is based on finding a simultaneous block diagonalization of the matrices encoding the synchronization pattern and the network topology. As an application, we use simultaneous block diagonalization to unveil an intriguing type of chimera states that appear only in the presence of higher-order interactions. The unified framework established here can be extended to other dynamical processes and can facilitate the discovery of emergent phenomena in complex systems with generalized interactions.

Block-diagonalization of the variational nodal response matrix using the symmetry group theory

2017 ◽  
Vol 351 ◽  
pp. 230-253 ◽  
Author(s):  
Zhipeng Li ◽  
Hongchun Wu ◽  
Yunzhao Li ◽  
Liangzhi Cao
Keyword(s):  
Group Theory ◽  
Symmetry Group ◽  
Response Matrix ◽  
Block Diagonalization
Sign in / Sign up

Export Citation Format

Share Document