39 research outputs found
Chimera Ising Walls in Forced Nonlocally Coupled Oscillators
Nonlocally coupled oscillator systems can exhibit an exotic spatiotemporal
structure called chimera, where the system splits into two groups of
oscillators with sharp boundaries, one of which is phase-locked and the other
is phase-randomized. Two examples of the chimera states are known: the first
one appears in a ring of phase oscillators, and the second one is associated
with the two-dimensional rotating spiral waves. In this article, we report yet
another example of the chimera state that is associated with the so-called
Ising walls in one-dimensional spatially extended systems, which is exhibited
by a nonlocally coupled complex Ginzburg-Landau equation with external forcing.Comment: 7 pages, 5 figures, to appear in Phys. Rev.
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
Hole Structures in Nonlocally Coupled Noisy Phase Oscillators
We demonstrate that a system of nonlocally coupled noisy phase oscillators
can collectively exhibit a hole structure, which manifests itself in the
spatial phase distribution of the oscillators. The phase model is described by
a nonlinear Fokker-Planck equation, which can be reduced to the complex
Ginzburg-Landau equation near the Hopf bifurcation point of the uniform
solution. By numerical simulations, we show that the hole structure clearly
appears in the space-dependent order parameter, which corresponds to the
Nozaki-Bekki hole solution of the complex Ginzburg-Landau equation.Comment: 4 pages, 4 figures, to appear in Phys. Rev.
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
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
Onset of Collective Oscillation in Chemical Turbulence under Global Feedback
Preceding the complete suppression of chemical turbulence by means of global
feedback, a different universal type of transition, which is characterized by
the emergence of small-amplitude collective oscillation with strong turbulent
background, is shown to occur at much weaker feedback intensity. We illustrate
this fact numerically in combination with a phenomenological argument based on
the complex Ginzburg-Landau equation with global feedback.Comment: 6 pages, 8 figures; to appear in Phys. Rev.
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.Comment: 23 pages, 17 figures, to appear in Phys. Rev.
Collective fluctuations in networks of noisy components
Collective dynamics result from interactions among noisy dynamical
components. Examples include heartbeats, circadian rhythms, and various pattern
formations. Because of noise in each component, collective dynamics inevitably
involve fluctuations, which may crucially affect functioning of the system.
However, the relation between the fluctuations in isolated individual
components and those in collective dynamics is unclear. Here we study a linear
dynamical system of networked components subjected to independent Gaussian
noise and analytically show that the connectivity of networks determines the
intensity of fluctuations in the collective dynamics. Remarkably, in general
directed networks including scale-free networks, the fluctuations decrease more
slowly with the system size than the standard law stated by the central limit
theorem. They even remain finite for a large system size when global
directionality of the network exists. Moreover, such nontrivial behavior
appears even in undirected networks when nonlinear dynamical systems are
considered. We demonstrate it with a coupled oscillator system.Comment: 5 figure
Phase synchronization between collective rhythms of globally coupled oscillator groups: noisy identical case
We theoretically investigate collective phase synchronization between
interacting groups of globally coupled noisy identical phase oscillators
exhibiting macroscopic rhythms. Using the phase reduction method, we derive
coupled collective phase equations describing the macroscopic rhythms of the
groups from microscopic Langevin phase equations of the individual oscillators
via nonlinear Fokker-Planck equations. For sinusoidal microscopic coupling, we
determine the type of the collective phase coupling function, i.e., whether the
groups exhibit in-phase or anti-phase synchronization. We show that the
macroscopic rhythms can exhibit effective anti-phase synchronization even if
the microscopic phase coupling between the groups is in-phase, and vice versa.
Moreover, near the onset of collective oscillations, we analytically obtain the
collective phase coupling function using center-manifold and phase reductions
of the nonlinear Fokker-Planck equations.Comment: 15 pages, 7 figure
Structure of Cell Networks Critically Determines Oscillation Regularity
Biological rhythms are generated by pacemaker organs, such as the heart
pacemaker organ (the sinoatrial node) and the master clock of the circadian
rhythms (the suprachiasmatic nucleus), which are composed of a network of
autonomously oscillatory cells. Such biological rhythms have notable
periodicity despite the internal and external noise present in each cell.
Previous experimental studies indicate that the regularity of oscillatory
dynamics is enhanced when noisy oscillators interact and become synchronized.
This effect, called the collective enhancement of temporal precision, has been
studied theoretically using particular assumptions. In this study, we propose a
general theoretical framework that enables us to understand the dependence of
temporal precision on network parameters including size, connectivity, and
coupling intensity; this effect has been poorly understood to date. Our
framework is based on a phase oscillator model that is applicable to general
oscillator networks with any coupling mechanism if coupling and noise are
sufficiently weak. In particular, we can manage general directed and weighted
networks. We quantify the precision of the activity of a single cell and the
mean activity of an arbitrary subset of cells. We find that, in general
undirected networks, the standard deviation of cycle-to-cycle periods scales
with the system size as , but only up to a certain system size
that depends on network parameters. Enhancement of temporal precision is
ineffective when . We also reveal the advantage of long-range
interactions among cells to temporal precision