139 research outputs found
Dynamics of conduction blocks in a model of paced cardiac tissue
We study numerically the dynamics of conduction blocks using a detailed
electrophysiological model. We find that this dynamics depends critically on
the size of the paced region. Small pacing regions lead to stationary
conduction blocks while larger pacing regions can lead to conduction blocks
that travel periodically towards the pacing region. We show that this
size-dependence dynamics can lead to a novel arrhythmogenic mechanism.
Furthermore, we show that the essential phenomena can be captured in a much
simpler coupled-map model.Comment: 8 pages 6 figure
Noise Induced Coherence in Neural Networks
We investigate numerically the dynamics of large networks of globally
pulse-coupled integrate and fire neurons in a noise-induced synchronized state.
The powerspectrum of an individual element within the network is shown to
exhibit in the thermodynamic limit () a broadband peak and an
additional delta-function peak that is absent from the powerspectrum of an
isolated element. The powerspectrum of the mean output signal only exhibits the
delta-function peak. These results are explained analytically in an exactly
soluble oscillator model with global phase coupling.Comment: 4 pages ReVTeX and 3 postscript figure
Excitable Dynamics in the Presence of Time Delay
The spiking properties of a subcritical Hopf oscillator with a time delayed
nonlinear feedback is investigated. Finite time delay is found to significantly
affect both the statistics and the fine structure of the spiking behavior.
These dynamical changes are explained in terms of the fundamental modifications
occurring in the bifurcation scenario of the system. Our mathematical model can
find useful applications in understanding the dynamical behaviour of various
real life excitable systems where propagation delay effects are ubiquitous.Comment: 10 pages including 7 figure
Coherence Resonance and Noise-Induced Synchronization in Globally Coupled Hodgkin-Huxley Neurons
The coherence resonance (CR) of globally coupled Hodgkin-Huxley neurons is
studied. When the neurons are set in the subthreshold regime near the firing
threshold, the additive noise induces limit cycles. The coherence of the system
is optimized by the noise. A bell-shaped curve is found for the peak height of
power spectra of the spike train, being significantly different from a
monotonic behavior for the single neuron. The coupling of the network can
enhance CR in two different ways. In particular, when the coupling is strong
enough, the synchronization of the system is induced and optimized by the
noise. This synchronization leads to a high and wide plateau in the local
measure of coherence curve. The local-noise-induced limit cycle can evolve to a
refined spatiotemporal order through the dynamical optimization among the
autonomous oscillation of an individual neuron, the coupling of the network,
and the local noise.Comment: five pages, five figure
Resonance between Noise and Delay
We propose here a stochastic binary element whose transition rate depends on
its state at a fixed interval in the past. With this delayed stochastic
transition this is one of the simplest dynamical models under the influence of
``noise'' and ``delay''. We demonstrate numerically and analytically that we
can observe resonant phenomena between the oscillatory behavior due to noise
and that due to delay.Comment: 4 pages, 5 figures, submitted to Phys.Rev.Lett Expanded and Added
Reference
Phase synchronization and noise-induced resonance in systems of coupled oscillators
We study synchronization and noise-induced resonance phenomena in systems of
globally coupled oscillators, each possessing finite inertia. The behavior of
the order parameter, which measures collective synchronization of the system,
is investigated as the noise level and the coupling strength are varied, and
hysteretic behavior is manifested. The power spectrum of the phase velocity is
also examined and the quality factor as well as the response function is
obtained to reveal noise-induced resonance behavior.Comment: to be published in Phys. Rev.
Effect of External Noise Correlation in Optical Coherence Resonance
Coherence resonance occurring in semiconductor lasers with optical feedback
is studied via the Lang-Kobayashi model with external non-white noise in the
pumping current. The temporal correlation and the amplitude of the noise have a
highly relevant influence in the system, leading to an optimal coherent
response for suitable values of both the noise amplitude and correlation time.
This phenomenon is quantitatively characterized by means of several statistical
measures.Comment: RevTeX, 4 pages, 7 figure
Scroll waves in isotropic excitable media : linear instabilities, bifurcations and restabilized states
Scroll waves are three-dimensional analogs of spiral waves. The linear
stability spectrum of untwisted and twisted scroll waves is computed for a
two-variable reaction-diffusion model of an excitable medium. Different bands
of modes are seen to be unstable in different regions of parameter space. The
corresponding bifurcations and bifurcated states are characterized by
performing direct numerical simulations. In addition, computations of the
adjoint linear stability operator eigenmodes are also performed and serve to
obtain a number of matrix elements characterizing the long-wavelength
deformations of scroll waves.Comment: 30 pages 16 figures, submitted to Phys. Rev.
Self-organized Vortex State in Two-dimensional Dictyostelium Dynamics
We present results of experiments on the dynamics of Dictyostelium discoideum
in a novel set-up which constraints cell motion to a plane. After aggregation,
the amoebae collect into round ''pancake" structures in which the cells rotate
around the center of the pancake. This vortex state persists for many hours and
we have explicitly verified that the motion is not due to rotating waves of
cAMP. To provide an alternative mechanism for the self-organization of the
Dictyostelium cells, we have developed a new model of the dynamics of
self-propelled deformable objects. In this model, we show that cohesive energy
between the cells, together with a coupling between the self-generated
propulsive force and the cell's configuration produces a self-organized vortex
state. The angular velocity profiles of the experiment and of the model are
qualitatively similar. The mechanism for self-organization reported here can
possibly explain similar vortex states in other biological systems.Comment: submitted to PRL; revised version dated 3/8/9
Pattern formation in directional solidification under shear flow. I: Linear stability analysis and basic patterns
An asymptotic interface equation for directional solidification near the
absolute stabiliy limit is extended by a nonlocal term describing a shear flow
parallel to the interface. In the long-wave limit considered, the flow acts
destabilizing on a planar interface. Moreover, linear stability analysis
suggests that the morphology diagram is modified by the flow near the onset of
the Mullins-Sekerka instability. Via numerical analysis, the bifurcation
structure of the system is shown to change. Besides the known hexagonal cells,
structures consisting of stripes arise. Due to its symmetry-breaking
properties, the flow term induces a lateral drift of the whole pattern, once
the instability has become active. The drift velocity is measured numerically
and described analytically in the framework of a linear analysis. At large flow
strength, the linear description breaks down, which is accompanied by a
transition to flow-dominated morphologies, described in a companion paper.
Small and intermediate flows lead to increased order in the lattice structure
of the pattern, facilitating the elimination of defects. Locally oscillating
structures appear closer to the instability threshold with flow than without.Comment: 20 pages, Latex, accepted for Physical Review
- …