ISSN:
1573-0689
Keywords:
phase-resetting
;
phase singularity
;
black hole
;
Fokker-Planck equation
;
Langevin equation
;
synchronization
;
stimulation
;
tremor
Source:
Springer Online Journal Archives 1860-2000
Topics:
Biology
,
Physics
Notes:
Abstract We present a stochastic approach to phase-resetting of an ensemble of oscillators. In order to describe stimulation-induced dynamical phenomena we develop a stochastic model which consists of an ensemble of phase oscillators interacting via random forces. Every single oscillator is submitted to a phase stimulus. The ensemble's dynamics is determined by a Fokker-Planck equation. The stationary states are calculated explicitly, whereas the transients are analysed numerically. If the stimulus of a given (non-vanishing) intensity is administered at a critical initial cluster phase for a critical duration T crit the ensemble's synchronized oscillation is annihilated. A transition from type 1 resetting to type 0 resetting occurs when the stimulation duration exceeds T crit. Stimulation causes a shift of the mean frequency of every single oscillator. This frequency shift is explicitly calculated by deriving the mean first passage time. The model shows that there is a subcritical intensity which is connected with an enhanced vulnerability to stimulation. The desynchronized states, the so-called black holes, are typically associated with a double peak in the ensemble's phase distribution. This is important for analysing experimental data because simple peak-detection algorithms are not able to extract the underlying dynamics. Our results are discussed from the experimentator's point of view so that the insights derived from our model can improve data analysis and design of stimulation experiments.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00383820
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