DocumentCode :
1756122
Title :
Synchronization and Consensus in State-Dependent Networks
Author :
Bogojeska, Aleksandra ; Mirchev, Miroslav ; Mishkovski, Igor ; Kocarev, Ljupco
Author_Institution :
Fac. of Comput. Sci. & Eng., Ss. Cyril and Methodius Univ., Skopje, Macedonia
Volume :
61
Issue :
2
fYear :
2014
fDate :
Feb. 2014
Firstpage :
522
Lastpage :
529
Abstract :
We study synchronization and consensus phenomena in state-dependent graphs in which the edges are weighted according to the Hebbian learning rule or its modified version. By exploring the master stability function of the synchronous state, we show that the modified Hebbian function as coupling strength enlarges the stability region of the synchronous state. In terms of consensus, given that the state-dependent weights are always positive, we prove that consensus in a network of multi-agent systems is always reachable. Furthermore, we show that in state-dependent graphs the second smallest eigenvalue of the graph Laplacian matrix has larger values due to the state-dependency, resulting in speed up of the convergence process.
Keywords :
Hebbian learning; convergence; matrix algebra; multi-agent systems; network theory (graphs); synchronisation; Hebbian learning rule; consensus phenomenon; convergence process; coupling strength; graph Laplacian matrix; graph edge; master stability function; multi-agent systems; stability region; state-dependent graphs; state-dependent networks; state-dependent weights; synchronization phenomenon; synchronous state; Couplings; Eigenvalues and eigenfunctions; Laplace equations; Neurons; Oscillators; Stability analysis; Synchronization; Adaptive coupling; Hebbian learning rule; consensus; master-stability function; state-dependent graphs; synchronization;
fLanguage :
English
Journal_Title :
Circuits and Systems I: Regular Papers, IEEE Transactions on
Publisher :
ieee
ISSN :
1549-8328
Type :
jour
DOI :
10.1109/TCSI.2013.2278351
Filename :
6583325
Link To Document :
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