The phenomenon of effective phase synchronization in stochastic oscillatory systems can be quantified by an average frequency and a phase diffusion coefficient. A different approach to compute the noise-averaged frequency is put forward. The method is based on a threshold crossing rate pioneered by Rice. After the introduction of the Rice frequency for noisy systems we compare this quantifier with those obtained in the context of other phase concepts, such as the natural and the Hilbert phase, respectively. It is demonstrated that the average Rice frequency
Nonlinear scalar third-order differential equation or jerky dynamics J (x,ẋ,ẍ) have recently attracted considerable interest since they constitute an important tool to identify and classify elementary chaotic flows. We investigate whether and under what conditions such systems can be synchronized by various coupling schemes such as the methods of PecoraCarroll and Cuomo-Oppenheim, BK-coupling and active-passive decomposition. In particular, for the latter two schemes, we present specific, simplified coupling or decomposition approaches that allow for analytical estimates of the rapidity of the synchronization error.
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