107 research outputs found
Reproducibility of a noisy limit-cycle oscillator induced by a fluctuating input
Reproducibility of a noisy limit-cycle oscillator driven by a random
piecewise constant signal is analyzed. By reducing the model to random phase
maps, it is shown that the reproducibility of the limit cycle generally
improves when the phase maps are monotonically increasing.Comment: 4 pages, 3 figures, Prog. Theoret. Phys. Suppl. 200
Phase coherence in an ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses
An ensemble of uncoupled limit-cycle oscillators receiving common Poisson
impulses shows a range of non-trivial behavior, from synchronization,
desynchronization, to clustering. The group behavior that arises in the
ensemble can be predicted from the phase response of a single oscillator to a
given impulsive perturbation. We present a theory based on phase reduction of a
jump stochastic process describing a Poisson-driven limit-cycle oscillator, and
verify the results through numerical simula- tions and electric circuit
experiments. We also give a geometrical interpretation of the synchronizing
mechanism, a perturbative expansion to the stationary phase distribution, and
the diffusion limit of our jump stochastic model
Collective Phase Sensitivity
The collective phase response to a macroscopic external perturbation of a
population of interacting nonlinear elements exhibiting collective oscillations
is formulated for the case of globally-coupled oscillators. The macroscopic
phase sensitivity is derived from the microscopic phase sensitivity of the
constituent oscillators by a two-step phase reduction. We apply this result to
quantify the stability of the macroscopic common-noise induced synchronization
of two uncoupled populations of oscillators undergoing coherent collective
oscillations.Comment: 6 pages, 3 figure
Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators
We study synchronization properties of general uncoupled limit-cycle
oscillators driven by common and independent Gaussian white noises. Using phase
reduction and averaging methods, we analytically derive the stationary
distribution of the phase difference between oscillators for weak noise
intensity. We demonstrate that in addition to synchronization, clustering, or
more generally coherence, always results from arbitrary initial conditions,
irrespective of the details of the oscillators.Comment: 6 pages, 2 figure
Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses
Populations of uncoupled limit-cycle oscillators receiving common random
impulses show various types of phase-coherent states, which are characterized
by the distribution of phase differences between pairs of oscillators. We
develop a theory to predict the stationary distribution of pairwise phase
difference from the phase response curve, which quantitatively encapsulates the
oscillator dynamics, via averaging of the Frobenius-Perron equation describing
the impulse-driven oscillators. The validity of our theory is confirmed by
direct numerical simulations using the FitzHugh-Nagumo neural oscillator
receiving common Poisson impulses as an example
Collective dynamical response of coupled oscillators with any network structure
We formulate a reduction theory that describes the response of an oscillator
network as a whole to external forcing applied nonuniformly to its constituent
oscillators. The phase description of multiple oscillator networks coupled
weakly is also developed. General formulae for the collective phase sensitivity
and the effective phase coupling between the oscillator networks are found. Our
theory is applicable to a wide variety of oscillator networks undergoing
frequency synchronization. Any network structure can systematically be treated.
A few examples are given to illustrate our theory.Comment: 4 pages, 2 figure
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