

Preprint 66/2006
Synchronization analysis of linearly coupled systems described by differential equations with a coupling delay
Wenlian Lu, Tianping Chen, and Guanron Chen
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Submission date: 24. Jul. 2006
Pages: 52
published in: Physica / D, 221 (2006) 2, p. 118-134
DOI number (of the published article): 10.1016/j.physd.2006.07.020
Bibtex
PACS-Numbers: 05.45.Xt, 02.30.Ks
Keywords and phrases: Synchronization space, Transverse space, Coupling delay, Local synchronization, Global synchronization
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Abstract:
When a transmission delay occurs in the interconnection of
linearly coupled systems described by ordinary differential
equations (LCODEs), both synchronization and the final
synchronized state will vary. In this paper, mathematical analysis
is presented on the synchronization phenomena of LCODEs with a
single coupling delay. Criteria are derived for both local and
global synchronization. It is known that addition to the dynamical
behaviors of the underlying uncoupled system and the coupling
configuration, the coupling strength and the coupling delay also
play key roles on the stability of synchronization. Both
theoretical and numerical analysis indicate that under some
conditions, if the coupling strength is large enough, the coupled
system can be completely synchronized for any coupling delays. On
the other hand, in some case, the coupled system can be
synchronized if the coupling delay is small enough.