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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
57/2009

Synchronization in discrete-time networks with general pairwise coupling

Frank Bauer, Fatihcan M. Atay and Jürgen Jost

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.

Received:
Sep 10, 2009
Published:
Sep 22, 2009
MSC Codes:
05C50, 37D45, 37E05, 39A11
PACS:
05.45.-a, 05.45.Ra, 05.45.Xt

Related publications

inJournal
2009 Repository Open Access
Frank Bauer, Fatihcan M. Atay and Jürgen Jost

Synchronization in discrete-time networks with general pairwise coupling

In: Nonlinearity, 22 (2009) 10, pp. 2333-2351