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MiS Preprint

Patterns from bifurcations: A symmetry analysis of networks with delayed coupling

Fatihcan M. Atay and Haibo Ruan


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.

MSC Codes:
15A18, 34C14, 34C23
02.30.Oz, 31.30.-j
symmetry, equivariant degree, bifurcation theory, delay, dynamical patterns

Related publications

2015 Repository Open Access
Fatihcan M. Atay and Haibo Ruan

Symmetry analysis of coupled scalar systems under time delay

In: Nonlinearity, 28 (2015) 3, pp. 795-824