

Preprint 57/2009
Synchronization in discrete-time networks with general pairwise coupling
Frank Bauer, Fatihcan M. Atay, and Jürgen Jost
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Submission date: 10. Sep. 2009
Pages: 24
published in: Nonlinearity, 22 (2009) 10, p. 2333-2351
DOI number (of the published article): 10.1088/0951-7715/22/10/001
Bibtex
MSC-Numbers: 05C50, 37D45, 37E05, 39A11
PACS-Numbers: 05.45.-a, 05.45.Ra, 05.45.Xt
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Abstract:
We consider complete synchronization of identical maps coupled
through a general interaction function and in a general network
topology where the edges may be directed and may carry both positive
and negative weights. We define mixed transverse exponents and derive sufficient
conditions for local complete synchronization. The general
non-diffusive coupling scheme can lead to new synchronous behavior, in networks of
identical units, that cannot be produced by single units in
isolation. In particular, we show that synchronous chaos can emerge
in networks of simple units. Conversely, in networks of chaotic
units simple synchronous dynamics can emerge; that is, chaos can be
suppressed through synchrony.