

Preprint 101/2003
Delays, connection topology, and synchronization of coupled chaotic maps
Fatihcan M. Atay, Jürgen Jost, and Andreas Wende
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Submission date: 08. Dec. 2003 (revised version: February 2004)
Pages: 7
published in: Physical review letters, 92 (2004) 14, art-no. 144101
DOI number (of the published article): 10.1103/PhysRevLett.92.144101
Bibtex
PACS-Numbers: 05.45.Ra, 05.45.Xt, 89.75.-k
Keywords and phrases: synchronization, time delay, coupled map lattices
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Abstract:
We consider networks of coupled maps where the connections between
units involve time delays. We show that, similar to the undelayed case,
the synchronization of the network depends on
the connection topology,
characterized by the spectrum of the graph Laplacian.
Consequently, scale-free and random networks are capable of synchronizing despite
the delayed flow of information, whereas regular networks with
nearest-neighbor connections and their small-world variants exhibit poor
synchronization. On the other hand, the connection delays can actually be conducive
to synchronization, so that it is possible for the delayed system to
synchronize where the undelayed system does not.
Furthermore, the delays determine the synchronized dynamics,
leading to the emergence of a wide range of new collective behavior
which the individual units are incapable of producing in isolation.
In this way, connection delays enable the overall system to
develop and sustain
new
dynamics through the coordination of its constituent units.