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

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September 2008, 10(4): 973-996. doi: 10.3934/dcdsb.2008.10.973

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

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

Received July 2007 Revised November 2007 Published August 2008

Abstract
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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.

Keywords: Master stability function, Lyapunov exponents., Synchronization.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.

Citation: R. Yamapi, R.S. MacKay. Stability of synchronization in a shift-invariant ring of mutually coupled oscillators. Discrete & Continuous Dynamical Systems - B, 2008, 10 (4) : 973-996. doi: 10.3934/dcdsb.2008.10.973

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