395 research outputs found
Spontaneous phase oscillation induced by inertia and time delay
We consider a system of coupled oscillators with finite inertia and
time-delayed interaction, and investigate the interplay between inertia and
delay both analytically and numerically. The phase velocity of the system is
examined; revealed in numerical simulations is emergence of spontaneous phase
oscillation without external driving, which turns out to be in good agreement
with analytical results derived in the strong-coupling limit. Such
self-oscillation is found to suppress synchronization and its frequency is
observed to decrease with inertia and delay. We obtain the phase diagram, which
displays oscillatory and stationary phases in the appropriate regions of the
parameters.Comment: 5 pages, 6 figures, to pe published in PR
A statistical mechanics of an oscillator associative memory with scattered natural frequencies
Analytic treatment of a non-equilibrium random system with large degrees of
freedoms is one of most important problems of physics. However, little research
has been done on this problem as far as we know. In this paper, we propose a
new mean field theory that can treat a general class of a non-equilibrium
random system. We apply the present theory to an analysis for an associative
memory with oscillatory elements, which is a well-known typical random system
with large degrees of freedoms.Comment: 8 pages, 4 figure
Partially and Fully Frustrated Coupled Oscillators With Random Pinning Fields
We have studied two specific models of frustrated and disordered coupled
Kuramoto oscillators, all driven with the same natural frequency, in the
presence of random external pinning fields. Our models are structurally
similar, but differ in their degree of bond frustration and in their finite
size ground state properties (one has random ferro- and anti-ferromagnetic
interactions; the other has random chiral interactions). We have calculated the
equilibrium properties of both models in the thermodynamic limit using the
replica method, with emphasis on the role played by symmetries of the pinning
field distribution, leading to explicit predictions for observables,
transitions, and phase diagrams. For absent pinning fields our two models are
found to behave identically, but pinning fields (provided with appropriate
statistical properties) break this symmetry. Simulation data lend satisfactory
support to our theoretical predictions.Comment: 37 pages, 7 postscript figure
Scaling and singularities in the entrainment of globally-coupled oscillators
The onset of collective behavior in a population of globally coupled
oscillators with randomly distributed frequencies is studied for phase
dynamical models with arbitrary coupling. The population is described by a
Fokker-Planck equation for the distribution of phases which includes the
diffusive effect of noise in the oscillator frequencies. The bifurcation from
the phase-incoherent state is analyzed using amplitude equations for the
unstable modes with particular attention to the dependence of the nonlinearly
saturated mode on the linear growth rate . In general
we find where is the
diffusion coefficient and is the mode number of the unstable mode. The
unusual factor arises from a singularity in the cubic term of
the amplitude equation.Comment: 11 pages (Revtex); paper submitted to Phys. Rev. Let
Coupled Oscillators with Chemotaxis
A simple coupled oscillator system with chemotaxis is introduced to study
morphogenesis of cellular slime molds. The model successfuly explains the
migration of pseudoplasmodium which has been experimentally predicted to be
lead by cells with higher intrinsic frequencies. Results obtained predict that
its velocity attains its maximum value in the interface region between total
locking and partial locking and also suggest possible roles played by partial
synchrony during multicellular development.Comment: 4 pages, 5 figures, latex using jpsj.sty and epsf.sty, to appear in
J. Phys. Soc. Jpn. 67 (1998
Synchronization in a System of Globally Coupled Oscillators with Time Delay
We study the synchronization phenomena in a system of globally coupled
oscillators with time delay in the coupling. The self-consistency equations for
the order parameter are derived, which depend explicitly on the amount of
delay. Analysis of these equations reveals that the system in general exhibits
discontinuous transitions in addition to the usual continuous transition,
between the incoherent state and a multitude of coherent states with different
synchronization frequencies. In particular, the phase diagram is obtained on
the plane of the coupling strength and the delay time, and ubiquity of
multistability as well as suppression of the synchronization frequency is
manifested. Numerical simulations are also performed to give consistent
results
Synchronization and resonance in a driven system of coupled oscillators
We study the noise effects in a driven system of globally coupled
oscillators, with particular attention to the interplay between driving and
noise. The self-consistency equation for the order parameter, which measures
the collective synchronization of the system, is derived; it is found that the
total order parameter decreases monotonically with noise, indicating overall
suppression of synchronization. Still, for large coupling strengths, there
exists an optimal noise level at which the periodic (ac) component of the order
parameter reaches its maximum. The response of the phase velocity is also
examined and found to display resonance behavior.Comment: 17 pages, 3 figure
Bifurcations in Globally Coupled Map Lattices
The dynamics of globally coupled map lattices can be described in terms of a
nonlinear Frobenius--Perron equation in the limit of large system size. This
approach allows for an analytical computation of stationary states and their
stability. The complete bifurcation behaviour of coupled tent maps near the
chaotic band merging point is presented. Furthermore the time independent
states of coupled logistic equations are analyzed. The bifurcation diagram of
the uncoupled map carries over to the map lattice. The analytical results are
supplemented with numerical simulations.Comment: 19 pages, .dvi and postscrip
Linear sampling method for identifying cavities in a heat conductor
We consider an inverse problem of identifying the unknown cavities in a heat
conductor. Using the Neumann-to-Dirichlet map as an input data, we develop a
linear sampling type method for the heat equation. A new feature is that there
is a freedom to choose the time variable, which suggests that we have more data
than the linear sampling methods for the inverse boundary value problem
associated with EIT and inverse scattering problem with near field data
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