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Precision of collective oscillations in complex dynamical systems with noise
Fumito Mori1, Alexander S Mikhailov1,2
1Department of Physical Chemistry, Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany.
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.
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