On a conjecture regarding the synchronization in an array of linearly coupled dynamical systems

Author

Wu, Chai Wah ; Chua, Leon O.

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., California Univ., Berkeley, CA, USA

Volume

43

Issue

2

fYear

1996

fDate

2/1/1996 12:00:00 AM

Firstpage

161

Lastpage

165

Abstract

In this letter, we give supporting evidence for a conjecture regarding the amount of coupling needed to synchronize an array of linearly coupled dynamical systems. Roughly speaking, the conjecture says that the coupling needed to synchronize an array of coupled systems is inversely proportional to the nonzero eigenvalue of the coupling graph that is smallest in magnitude. The conjecture implies that the coupling needed to synchronize an array can be derived from the coupling topology and the coupling needed to synchronize two coupled dynamical systems

Keywords

Chua´s circuit; coupled circuits; eigenvalues and eigenfunctions; network topology; nonlinear network analysis; oscillators; synchronisation; Chua´s oscillators; Laplacian matrix; coupling graph; coupling topology; linearly coupled dynamical systems; nonzero eigenvalue; synchronization; Application software; Coupling circuits; Eigenvalues and eigenfunctions; H infinity control; Laplace equations; Numerical simulation; Oscillators; Resistors; Sufficient conditions; Topology;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.486440

Filename

486440