Showing papers by "Hiroya Nakao published in 2008"

Collective phase sensitivity.

Abstract: 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.

Phase coherence in an ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses

Abstract: An ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses shows a range of nontrivial 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 simulations 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.

Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses

Abstract: 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 differences from the phase response curve, which quantitatively encapsulates the oscillator dynamics, via averaging of the FrobeniusPerron 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.

Comment on "Phase Reduction of Stochastic Limit Cycle Oscillators"

Abstract: In a recent Letter, Yoshimura and Arai [1] claimed that the conventional phase stochastic differential equation(SDE) used in [2, 3, 4] does not give a proper approximation to limit-cycle oscillators driven by noise, and proposeda modified phase SDE. Here we argue that their claim is not always correct; both SDEs are valid depending on thesituation.Since physical noise has an associated time scale and all oscillators have a characteristic rate of attraction, whichof the two SDEs is appropriate depends on the relative sizes of these two scales. As a simple example, let us considerthe Stuart-Landau (SL) model used in [1, 2] driven by a colored noise generated by the Ornstein-Uhlenbeck process(OUP) [5], which is rescaled such that the amplitude relaxation time explicitly appears while keeping the limit cycleand its isochrons invariant,W˙ (t) = {T