355 research outputs found
Global firing induced by network disorder in ensembles of active rotators
We study the influence of repulsive interactions on an ensemble of coupled
excitable rotators. We find that a moderate fraction of repulsive interactions
can trigger global firing of the ensemble. The regime of global firing,
however, is suppressed in sufficiently large systems if the network of
repulsive interactions is fully random, due to self-averaging in its degree
distribution. We thus introduce a model of partially random networks with a
broad degree distribution, where self-averaging due to size growth is absent.
In this case, the regime of global firing persists for large sizes. Our results
extend previous work on the constructive effects of diversity in the collective
dynamics of complex systems.Comment: 8 pages, 6 figure
N-tree approximation for the largest Lyapunov exponent of a coupled-map lattice
The N-tree approximation scheme, introduced in the context of random directed
polymers, is here applied to the computation of the maximum Lyapunov exponent
in a coupled map lattice. We discuss both an exact implementation for small
tree-depth and a numerical implementation for larger s. We find that the
phase-transition predicted by the mean field approach shifts towards larger
values of the coupling parameter when the depth is increased. We conjecture
that the transition eventually disappears.Comment: RevTeX, 15 pages,5 figure
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
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
Phase ordering on small-world networks with nearest-neighbor edges
We investigate global phase coherence in a system of coupled oscillators on a
small-world networks constructed from a ring with nearest-neighbor edges. The
effects of both thermal noise and quenched randomness on phase ordering are
examined and compared with the global coherence in the corresponding \xy model
without quenched randomness. It is found that in the appropriate regime phase
ordering emerges at finite temperatures, even for a tiny fraction of shortcuts.
Nature of the phase transition is also discussed.Comment: 5 pages, 4 figures, Phys. Rev. E (in press
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
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
Acceleration effect of coupled oscillator systems
We have developed a curved isochron clock (CIC) by modifying the radial
isochron clock to provide a clean example of the acceleration (deceleration)
effect. By analyzing a two-body system of coupled CICs, we determined that an
unbalanced mutual interaction caused by curved isochron sets is the minimum
mechanism needed for generating the acceleration (deceleration) effect in
coupled oscillator systems. From this we can see that the Sakaguchi and
Kuramoto (SK) model which is a class of non-frustrated mean feild model has an
acceleration (deceleration) effect mechanism. To study frustrated coupled
oscillator systems, we extended the SK model to two oscillator associative
memory models, one with symmetric and one with asymmetric dilution of coupling,
which also have the minimum mechanism of the acceleration (deceleration)
effect. We theoretically found that the {\it Onsager reaction term} (ORT),
which is unique to frustrated systems, plays an important role in the
acceleration (de! celeration) effect. These two models are ideal for evaluating
the effect of the ORT because, with the exception of the ORT, they have the
same order parameter equations. We found that the two models have identical
macroscopic properties, except for the acceleration effect caused by the ORT.
By comparing the results of the two models, we can extract the effect of the
ORT from only the rotation speeds of the oscillators.Comment: 35 pages, 10 figure
Solvable model of a phase oscillator network on a circle with infinite-range Mexican-hat-type interaction
We describe a solvable model of a phase oscillator network on a circle with
infinite-range Mexican-hat-type interaction. We derive self-consistent
equations of the order parameters and obtain three non-trivial solutions
characterized by the rotation number. We also derive relevant characteristics
such as the location-dependent distributions of the resultant frequencies of
desynchronized oscillators. Simulation results closely agree with the
theoretical ones
Oscillator neural network model with distributed native frequencies
We study associative memory of an oscillator neural network with distributed
native frequencies. The model is based on the use of the Hebb learning rule
with random patterns (), and the distribution function of
native frequencies is assumed to be symmetric with respect to its average.
Although the system with an extensive number of stored patterns is not allowed
to get entirely synchronized, long time behaviors of the macroscopic order
parameters describing partial synchronization phenomena can be obtained by
discarding the contribution from the desynchronized part of the system. The
oscillator network is shown to work as associative memory accompanied by
synchronized oscillations. A phase diagram representing properties of memory
retrieval is presented in terms of the parameters characterizing the native
frequency distribution. Our analytical calculations based on the
self-consistent signal-to-noise analysis are shown to be in excellent agreement
with numerical simulations, confirming the validity of our theoretical
treatment.Comment: 9 pages, revtex, 6 postscript figures, to be published in J. Phys.
- …