DocumentCode :
897602
Title :
Application of graph theory to the synchronization in an array of coupled nonlinear oscillators
Author :
Wu, Chai Wah ; Chua, Leon O.
Author_Institution :
Electron. Res. Lab., California Univ., Berkeley, CA, USA
Volume :
42
Issue :
8
fYear :
1995
fDate :
8/1/1995 12:00:00 AM
Firstpage :
494
Lastpage :
497
Abstract :
In this letter, we show how algebraic graph theory can be used to derive sufficient conditions for an array of resistively coupled nonlinear oscillators to synchronize. These conditions are derived from the connectivity graph, which describes how the oscillators are connected. In particular, we show how such a sufficient condition is dependent on the algebraic connectivity of the connectivity graph. Intuition tells us that if the oscillators are more “closely connected” to each other, then they are more likely to synchronize. We discuss how to quantify connectedness in graph-theoretical terms and its relation to algebraic connectivity and show that our results are in accordance with this intuition. We also give an upper bound on the coupling conductance required for synchronization for arbitrary graphs, which is in the order of n2 , where n is the number of oscillators
Keywords :
arrays; coupled circuits; graph theory; oscillators; synchronisation; algebraic graph theory; array; connectivity; coupling conductance; resistively coupled nonlinear oscillators; synchronization; Concrete; Coupling circuits; Ear; Graph theory; Integrated circuit interconnections; Oscillators; Resistors; Sufficient conditions; Terminology; Upper bound;
fLanguage :
English
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
Publisher :
ieee
ISSN :
1057-7122
Type :
jour
DOI :
10.1109/81.404064
Filename :
404064
Link To Document :
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