title: Noise-controlled oscillations and their bifurcations in coupled phase oscillators.
abstract: We derive in Gaussian approximation dynamical equations for the first two cumulants of the mean field fluctuations in a system of globally coupled stochastic phase oscillators. In these equations the intensity of noise serves as an explicit control parameter. Its variation generates transitions between three dynamical regimes: (i) stationary, (ii) rotatory and (iii) locally oscillatory (breathing). The latter regime has previously not been reported in studies of globally coupled noisy phase oscillators. Our detailed bifurcation analysis is supported by numerical simulations of an ensemble of coupled stochastic phase oscillators. Similar regimes are also found in simulations of globally coupled stochastic FitzHugh-Nagumo elements.
authors.affiliation: Institute of Physics, Humboldt-University of Berlin, Newtonstrasse 15, 12489 Berlin, Germany.
authors.forename: M A
authors.initials: MA
authors.lastname: Zaks
authors.forename: A B
authors.initials: AB
authors.lastname: Neiman
authors.forename: S
authors.initials: S
authors.lastname: Feistel
authors.forename: L
authors.initials: L
authors.lastname: Schimansky-Geier
mesh_terms: D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D005246:Feedback / Q000502:physiology*; D008954:Models, Biological; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*; D010507:Periodicity; D013269:Stochastic Processes