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Hiroya Nakao

Publications and source records attributed to Hiroya Nakao.

108 records · Page 6Linked to original sources
arXiv2009

Stochastic phase reduction for a general class of noisy limit cycle oscillators

We formulate a phase-reduction method for a general class of noisy limit cycle oscillators and find that the phase equation is parametrized by the ratio between time scales of the noise correlation and amplitude relaxation of the limit cycle. The equation naturally includes previously proposed and mutually exclusive phase equations as special cases. The validity of the theory is numerically confirmed. Using the method, we reveal how noise and its correlation time affect limit cycle oscillations.

nlin.AO↗
arXiv2009

Experimental synchronization of circuit oscillations induced by common telegraph noise

Experimental realization and quantitative investigation of common-noise-induced synchronization of limit-cycle oscillations subject to random telegraph signals are performed using an electronic oscillator circuit. Based on our previous formulation [K. Nagai et al., Phys. Rev. E 71, 036217 (2005)], dynamics of the circuit is described as random-phase mappings between two limit cycles. Lyapunov exponents characterizing the degree of synchronization are estimated from experimentally determined phase maps and compared with linear damping rates of phase differences measured directly. Noisy on-off intermittency of the phase difference as predicted by the theory is also confirmed experimentally.

nlin.AO↗
arXiv2009

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.

nlin.AO↗
arXiv2009

Diffusion-induced instability and chaos in random oscillator networks

We demonstrate that diffusively coupled limit-cycle oscillators on random networks can exhibit various complex dynamical patterns. Reducing the system to a network analog of the complex Ginzburg-Landau equation, we argue that uniform oscillations can be linearly unstable with respect to spontaneous phase modulations due to diffusional coupling - the effect corresponding to the Benjamin-Feir instability in continuous media. Numerical investigations under this instability in random scale-free networks reveal a wealth of complex dynamical regimes, including partial amplitude death, clustering, and chaos. A dynamic mean-field theory explaining different kinds of nonlinear dynamics is constructed.

nlin.PS↗
arXiv2008

Comment on "Phase Reduction of Stochastic Limit Cycle Oscillators"

This is a comment on a recent paper by Yoshimura and Arai [Phys. Rev. Lett. 101, 154101 (2008)] on phase reduction of noisy limit-cycle oscillators, in which the authors claimed that the conventional phase stochastic differential equation used in previous studies does not give a proper approximation and proposed a modified phase equation. Here we point out that both phase equations are valid depending on the situation. We argue that the relative size of amplitude relaxation time and noise correlation time determines which of the two equations is appropriate in the white-noise limit. The conventional phase equation is also a proper approximation to noisy limit cycles with sufficiently fast amplitude relaxation, which can be used as a starting point for further analysis.

nlin.AO↗
arXiv2008

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.

nlin.AO↗
arXiv2008

Turing patterns on networks

Turing patterns formed by activator-inhibitor systems on networks are considered. The linear stability analysis shows that the Turing instability generally occurs when the inhibitor diffuses sufficiently faster than the activator. Numerical simulations, using a prey-predator model on a scale-free random network, demonstrate that the final, asymptotically reached Turing patterns can be largely different from the critical modes at the onset of instability, and multistability and hysteresis are typically observed. An approximate mean-field theory of nonlinear Turing patterns on the networks is constructed.

nlin.PS↗
arXiv2008

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.

nlin.AO↗
arXiv2008

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.

nlin.AO↗
arXiv2007

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.

nlin.AO↗
arXiv2007

Noise-induced Turbulence in Nonlocally Coupled Oscillators

We demonstrate that nonlocally coupled limit-cycle oscillators subject to spatiotemporally white Gaussian noise can exhibit a noise-induced transition to turbulent states. After illustrating noise-induced turbulent states with numerical simulations using two representative models of limit-cycle oscillators, we develop a theory that clarifies the effective dynamical instabilities leading to the turbulent behavior using a hierarchy of dynamical reduction methods. We determine the parameter region where the system can exhibit noise-induced turbulent states, which is successfully confirmed by extensive numerical simulations at each level of the reduction.

nlin.CD↗
arXiv2006

Population coding by globally coupled phase oscillators

A system of globally coupled phase oscillators subject to an external input is considered as a simple model of neural circuits coding external stimulus. The information coding efficiency of the system in its asynchronous state is quantified using Fisher information. The effect of coupling and noise on the information coding efficiency in the stationary state is analyzed. The relaxation process of the system after the presentation of an external input is also studied. It is found that the information coding efficiency exhibits a large transient increase before the system relaxes to the final stationary state.

cond-mat.dis-nn↗
arXiv2000

Visualization of correlation cascade in spatio-temporal chaos using wavelets

We propose a simple method to visualize spatio-temporal correlation between scales using wavelets, and apply it to two typical spatio-temporally chaotic systems, namely to coupled complex Ginzburg-Landau oscillators with diffusive interaction, and those with non-local interaction. Reflecting the difference between underlying dynamical processes, our method provides distinctive results for those two systems. Especially, for the non-locally interacting case where the system exhibits fractal amplitude patterns and power-law spectrum, it clearly visualizes the dynamical cascade process of spatio-temporal correlation between scales.

nlin.CD↗
arXiv2000

Multi-scaling properties of truncated Levy flights

Multi-scaling properties of one-dimensional truncated Levy flights are studied. Due to the broken self-similarity of the distribution of jumps, they are expected to possess multi-scaling properties in contrast to the ordinary Levy flights. We argue this fact based on a smoothly truncated Levy distribution, and derive the functional form of the scaling exponents. Specifically, they exhibit bi-fractal behavior, which is the simplest case of multi-scaling.

cond-mat.stat-mech↗
arXiv1999

Anomalous spatio-temporal chaos in a two-dimensional system of non-locally coupled oscillators

A two-dimensional system of non-locally coupled complex Ginzburg-Landau oscillators is investigated numerically for the first time. As already known for the one-dimensional case, the system exhibits anomalous spatio-temporal chaos characterized by power-law spatial correlations. In this chaotic regime, the amplitude difference between neighboring elements shows temporal noisy on-off intermittency. The system is also spatially intermittent in this regime, which is revealed by multi-scaling analysis; the amplitude field is multi-affine and the difference field is multi-fractal. Correspondingly, the probability distribution function of the measure defined for each field is strongly non-Gaussian, showing scale-dependent deviations in the tails due to intermittency.

chao-dyn↗
arXiv1998

Asymptotic power law of moments in a random multiplicative process with weak additive noise

It is well known that a random multiplicative process with weak additive noise generates a power-law probability distribution. It has recently been recognized that this process exhibits another type of power law: the moment of the stochastic variable scales as a function of the additive noise strength. We clarify the mechanism for this power-law behavior of moments by treating a simple Langevin-type model both approximately and exactly, and argue this mechanism is universal. We also discuss the relevance of our findings to noisy on-off intermittency and to singular spatio-temporal chaos recently observed in systems of non-locally coupled elements.

cond-mat.stat-mech↗
arXiv1997

Universal Scaling Properties in Large Assemblies of Simple Dynamical Units Driven by Long-Wave Random Forcing

Large assemblies of nonlinear dynamical units driven by a long-wave fluctuating external field are found to generate strong turbulence with scaling properties. This type of turbulence is so robust that it persists over a finite parameter range with parameter-dependent exponents of singularity, and is insensitive to the specific nature of the dynamical units involved. Whether or not the units are coupled with their neighborhood is also unimportant. It is discovered numerically that the derivative of the field exhibits strong spatial intermittency with multifractal structure.

chao-dyn↗