Delay-induced stability: From oscillators to networks

Fatihcan M. Atay

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Submission date: 11. May. 2010
published in: Complex time-delay systems : theory and applications / F. M. Atay (ed.)
Berlin [u. a.] : Springer, 2010. - P. 45 - 62 
DOI number (of the published article): 10.1007/978-3-642-02329-3_2
Bibtex

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.