Paper Info
Title
Synchronization of discrete-time dynamical networks with time-varying couplings
Abstract
We study the local complete synchronization of discrete-time dynamical networks with time-varying couplings. Our conditions for the temporal variation of the couplings are rather general and include variations in both the network structure and the reaction dynamics; the reactions could, for example, be driven by a random dynamical system. A basic tool is the concept of the Hajnal diameter, which we extend to infinite Jacobian matrix sequences. The Hajnal diameter can be used to verify synchronization, and we show that it is equivalent to other quantities which have been extended to time-varying cases, such as the projection radius, projection Lyapunov exponents, and transverse Lyapunov exponents. Furthermore, these results are used to investigate the synchronization problem in coupled map networks with time-varying topologies and possibly directed and weighted edges. In this case, the Hajnal diameter of the infinite coupling matrices can be used to measure the synchronizability of the network process. As we show, the network is capable of synchronizing some chaotic map if and only if there exists an integer T > 0 such that for any time interval of length T, there exists a vertex which can access other vertices by directed paths in that time interval.
Year
DOI
Venue
2007
10.1137/060657935
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Keywords
Field
DocType
synchronization,dynamical networks,time-varying coupling,Hajnal diameter,projection joint spectral radius,Lyapunov exponents,spanning tree
Topology,Synchronization,Spectral radius,Jacobian matrix and determinant,Mathematical analysis,Matrix (mathematics),Random dynamical system,Discrete time and continuous time,Lyapunov exponent,Dynamical system,Mathematics
Journal
Volume
Issue
ISSN
39
4
0036-1410
Citations 
PageRank 
References 
30
1.66
6
Authors
3
Name
Order
Citations
PageRank
Wenlian Lu1133193.47
Fatihcan M. Atay216713.81
Jürgen Jost39512.39