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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
32/2011

On delay-induced stability in diffusively coupled discrete-time systems

Fatihcan M. Atay

Abstract

The stability of networked systems is considered under time-delayed diffusive coupling. Necessary conditions for stability are given for general directed and weighted networks with both positive and negative weights. Exact stability conditions are obtained for undirected networks with nonnegative weights, and it is shown that the largest eigenvalue of the graph Laplacian determines the e ffect of the connection topology on stability. It is further shown that the stability region in the parameter space shrinks with increasing values of the largest eigenvalue, or of the time delay of the same parity. In particular, unstable fixed points of the individual maps can be stabilized for certain parameter ranges when they are coupled with an odd time delay, provided that the connection structure is not bipartite. Furthermore, signal propagation delays are compared to signal processing delays and it is shown that delay induced stability cannot occur for the latter. Connections to continuous-time systems are indicated.

Received:
Jun 6, 2011
Published:
Jun 6, 2011
MSC Codes:
39A30, 94C15, 05C22
Keywords:
delay, stability, Signed graph, synchronization, chaos

Related publications

inJournal
2012 Repository Open Access
Fatihcan M. Atay

On delay-induced stability in diffusively coupled discrete-time systems

In: Afrika matematika, 23 (2012) 1, pp. 109-119