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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
25/2010

Delay-induced stability: From oscillators to networks

Fatihcan M. Atay

Abstract

We consider the stability of oscillatory systems near a supercritical Hopf bifurcation under the presence of time delays. We give a brief outline of averaging theory for functional differential equations and apply it to the stability of delayed-feedback systems as well as networks with connection delays. In the latter case, the effect of the network topology as well as the phenomena of total and partial amplitude death are addressed. Results are presented for both continuous and discrete time systems.

Received:
May 11, 2010
Published:
May 18, 2010

Related publications

inBook
2010 Repository Open Access
Fatihcan M. Atay

Delay-induced stability : from oscillators to networks

In: Complex time-delay systems : theory and applications / Fatihcan M. Atay (ed.)
Berlin [u. a.] : Springer, 2010. - pp. 45-62