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
110/2013
Patterns from bifurcations: A symmetry analysis of networks with delayed coupling
Fatihcan M. Atay and Haibo Ruan
Abstract
We study systems of coupled units in a general network configuration with a coupling delay. We show that the destabilizing bifurcations from an equilibrium are governed by the extreme eigenvalues of the coupling matrix of the network. Based on the equivariant degree method and its computational packages, we perform a symmetry classification of destabilizing bifurcations in bidirectional rings of coupled units, for bifurcating solutions either of steady-states or of oscillating states. We also introduce the concept of secondary dominating orbit types to capture bifurcating solutions of submaximal nature.
