Stability of synchronization in a shift-invariant ring of mutually coupled oscillators

R. Yamapi; R.S. MacKay

doi:10.3934/dcdsb.2008.10.973

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2008, Volume 10, Issue 4: 973-996. Doi: 10.3934/dcdsb.2008.10.973

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Stability of synchronization in a shift-invariant ring of mutually coupled oscillators

R. Yamapi^1, and
R.S. MacKay^2,

1.
Department of Physics, Faculty of Science, University of DOUALA, P.O. Box 24157, DOUALA
2.
Mathematics Institute, University of Warwick, Coventry, CV4 7AL

Received: June 30, 2007

Revised: October 31, 2007

Published: August 2008

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Abstract

This paper treats synchronization dynamics in a shift-invariant ring of N mutually coupled self-sustained electrical units. Via some qualitative theory for the Lyapunov exponents, we derive the regimes of coupling parameters for which synchronized oscillation is stable or unstable in the ring.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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