Periodic patterns in a ring of delay-coupled oscillators.

Perlikowski, P.; Popovych, O. V.; Yanchuk, S.; Tass, P.A.

doi:10.1103/PhysRevE.82.036208

Journal Article

PreJuSER-14629

Periodic patterns in a ring of delay-coupled oscillators.

Perlikowski, P. ; Yanchuk, S. ; Popovych, O. V.FZJ* ; Tass, P. A.FZJ*

2010
APS College Park, Md.

Physical review / E 82(3), 036208 (2010) [10.1103/PhysRevE.82.036208]

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Please use a persistent id in citations: http://hdl.handle.net/2128/9304 doi:10.1103/PhysRevE.82.036208

Abstract: We describe the appearance and stability of spatiotemporal periodic patterns (rotating waves) in unidirectional rings of coupled oscillators with delayed couplings. We show how delays in the coupling lead to the splitting of each rotating wave into several new ones. The appearance of rotating waves is mediated by the Hopf bifurcations of the symmetric equilibrium. We also conclude that the coupling delays can be effectively replaced by increasing the number of oscillators in the chain. The phenomena are shown for the Stuart-Landau oscillators as well as for the coupled FitzHugh-Nagumo systems modeling an ensemble of spiking neurons interacting via excitatory chemical synapses.

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Note: P.P. and S.Y. acknowledge the support of DFG Research Center Matheon "Mathematics for key technologies" under Project No. D21. P.P. acknowledges the support of Department of International Cooperation of Poland under Project No. DWM/N97/DAAD/2008 and from Foundation for Polish Science (the START Foundation)

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