title: Periodic patterns in a ring of delay-coupled oscillators.
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.
authors.affiliation: Institute of Mathematics, Humboldt University of Berlin, 10099 Berlin, Germany.
authors.forename: P
authors.initials: P
authors.lastname: Perlikowski
authors.forename: S
authors.initials: S
authors.lastname: Yanchuk
authors.forename: O V
authors.initials: OV
authors.lastname: Popovych
authors.forename: P A
authors.initials: PA
authors.lastname: Tass
mesh_terms: D008962:Models, Theoretical; D009474:Neurons / Q000166:cytology; D010507:Periodicity; D013997:Time Factors