scholarly journals Complete characterization of the stability of cluster synchronization in complex dynamical networks

2016 ◽  
Vol 2 (4) ◽  
pp. e1501737 ◽  
Author(s):  
Francesco Sorrentino ◽  
Louis M. Pecora ◽  
Aaron M. Hagerstrom ◽  
Thomas E. Murphy ◽  
Rajarshi Roy
Keyword(s):  
Group Theory ◽  
Complete Characterization ◽  
Power Grids ◽  
Cluster Synchronization ◽  
General Technique ◽  
Dynamical Networks ◽  
Computational Group Theory ◽  
Node Network ◽  
Engineered Systems ◽  
The Stability

Synchronization is an important and prevalent phenomenon in natural and engineered systems. In many dynamical networks, the coupling is balanced or adjusted to admit global synchronization, a condition called Laplacian coupling. Many networks exhibit incomplete synchronization, where two or more clusters of synchronization persist, and computational group theory has recently proved to be valuable in discovering these cluster states based on the topology of the network. In the important case of Laplacian coupling, additional synchronization patterns can exist that would not be predicted from the group theory analysis alone. Understanding how and when clusters form, merge, and persist is essential for understanding collective dynamics, synchronization, and failure mechanisms of complex networks such as electric power grids, distributed control networks, and autonomous swarming vehicles. We describe a method to find and analyze all of the possible cluster synchronization patterns in a Laplacian-coupled network, by applying methods of computational group theory to dynamically equivalent networks. We present a general technique to evaluate the stability of each of the dynamically valid cluster synchronization patterns. Our results are validated in an optoelectronic experiment on a five-node network that confirms the synchronization patterns predicted by the theory.

Applications of random graphs

2017 ◽  
Author(s):  
A.C.C. Coolen ◽  
A. Annibale ◽  
E.S. Roberts
Keyword(s):  
Social Networks ◽  
Random Graphs ◽  
Interaction Network ◽  
Power Grids ◽  
Protein Protein Interaction ◽  
Topological Features ◽  
First Case ◽  
The Stability ◽  
Protein Protein Interaction Network

This chapter reviews graph generation techniques in the context of applications. The first case study is power grids, where proposed strategies to prevent blackouts have been tested on tailored random graphs. The second case study is in social networks. Applications of random graphs to social networks are extremely wide ranging – the particular aspect looked at here is modelling the spread of disease on a social network – and how a particular construction based on projecting from a bipartite graph successfully captures some of the clustering observed in real social networks. The third case study is on null models of food webs, discussing the specific constraints relevant to this application, and the topological features which may contribute to the stability of an ecosystem. The final case study is taken from molecular biology, discussing the importance of unbiased graph sampling when considering if motifs are over-represented in a protein–protein interaction network.

scholarly journals Asymmetry underlies stability in power grids

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Ferenc Molnar ◽  
Takashi Nishikawa ◽  
Adilson E. Motter
Keyword(s):  
Symmetry Breaking ◽  
Real World ◽  
Power Grids ◽  
Stable Operation ◽  
World Systems ◽  
Symmetric State ◽  
Network Systems ◽  
Additional Improvement ◽  
The Stability ◽  
General Method

AbstractBehavioral homogeneity is often critical for the functioning of network systems of interacting entities. In power grids, whose stable operation requires generator frequencies to be synchronized—and thus homogeneous—across the network, previous work suggests that the stability of synchronous states can be improved by making the generators homogeneous. Here, we show that a substantial additional improvement is possible by instead making the generators suitably heterogeneous. We develop a general method for attributing this counterintuitive effect to converse symmetry breaking, a recently established phenomenon in which the system must be asymmetric to maintain a stable symmetric state. These findings constitute the first demonstration of converse symmetry breaking in real-world systems, and our method promises to enable identification of this phenomenon in other networks whose functions rely on behavioral homogeneity.

STABILITY OF TWO TYPICAL COMPLEX DYNAMICAL NETWORKS

2008 ◽  
Vol 22 (05) ◽  
pp. 553-560 ◽  
Author(s):  
WU-JIE YUAN ◽  
XIAO-SHU LUO ◽  
PIN-QUN JIANG ◽  
BING-HONG WANG ◽  
JIN-QING FANG
Keyword(s):  
Numerical Simulation ◽  
Dissipative System ◽  
Small World ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
General Complex ◽  
The Stability ◽  
Theoretical Results

When being constructed, complex dynamical networks can lose stability in the sense of Lyapunov (i. s. L.) due to positive feedback. Thus, there is much important worthiness in the theory and applications of complex dynamical networks to study the stability. In this paper, according to dissipative system criteria, we give the stability condition in general complex dynamical networks, especially, in NW small-world and BA scale-free networks. The results of theoretical analysis and numerical simulation show that the stability i. s. L. depends on the maximal connectivity of the network. Finally, we show a numerical example to verify our theoretical results.

Decentralized Adaptive Pinning Control for Cluster Synchronization of Complex Dynamical Networks

2013 ◽  
Vol 43 (1) ◽  
pp. 394-399 ◽  
Author(s):  
Housheng Su ◽  
Zhihai Rong ◽  
Michael Z. Q. Chen ◽  
Xiaofan Wang ◽  
Guanrong Chen ◽  
...  
Keyword(s):  
Pinning Control ◽  
Complex Dynamical Networks ◽  
Cluster Synchronization ◽  
Dynamical Networks

Robust H ∞ cluster synchronization analysis of Lurie dynamical networks

2014 ◽  
Vol 23 (4) ◽  
pp. 040501 ◽  
Author(s):  
Ling Guo ◽  
Xiao-Hong Nian ◽  
Huan Pan ◽  
Zhi-Tong Bing
Keyword(s):  
Cluster Synchronization ◽  
Dynamical Networks

Computational Group Theory

2011 ◽  
pp. 2113-2161
Author(s):  
Bettina Eick ◽  
Gerhard Hiß ◽  
Derek Holt ◽  
Eamonn O’Brien
Keyword(s):  
Group Theory ◽  
Computational Group Theory
Sign in / Sign up

Export Citation Format

Share Document