title: Precision of collective oscillations in complex dynamical systems with noise.
abstract: Two kinds of oscillation precision are investigated for complex oscillatory dynamical systems under action of noise. The many-cycle precision determined by the variance of the times needed for a large number of cycles is closely related to diffusion of the global oscillation phase and provides an invariant property of a system. The single-cycle precision given by the variance in durations of single cycles is sensitive to the choice of an output variable and output checkpoint; it can be improved by an appropriate selection of them. A general analysis of the precision properties based on the Floquet perturbation theory is performed and analytical predictions are verified in numerical simulations of a model oscillatory genetic network.
authors.affiliation: Department of Physical Chemistry, Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany.
authors.forename: Fumito
authors.initials: F
authors.lastname: Mori
authors.affiliation: Department of Physical Chemistry, Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany.|Department of Mathematical and Life Sciences, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan.
authors.forename: Alexander S
authors.initials: AS
authors.lastname: Mikhailov