1,196 research outputs found
Avalanche of Bifurcations and Hysteresis in a Model of Cellular Differentiation
Cellular differentiation in a developping organism is studied via a discrete
bistable reaction-diffusion model. A system of undifferentiated cells is
allowed to receive an inductive signal emenating from its environment.
Depending on the form of the nonlinear reaction kinetics, this signal can
trigger a series of bifurcations in the system. Differentiation starts at the
surface where the signal is received, and cells change type up to a given
distance, or under other conditions, the differentiation process propagates
through the whole domain. When the signal diminishes hysteresis is observed
Photo-excited semiconductor superlattices as constrained excitable media: Motion of dipole domains and current self-oscillations
A model for charge transport in undoped, photo-excited semiconductor
superlattices, which includes the dependence of the electron-hole recombination
on the electric field and on the photo-excitation intensity through the
field-dependent recombination coefficient, is proposed and analyzed. Under dc
voltage bias and high photo-excitation intensities, there appear self-sustained
oscillations of the current due to a repeated homogeneous nucleation of a
number of charge dipole waves inside the superlattice. In contrast to the case
of a constant recombination coefficient, nucleated dipole waves can split for a
field-dependent recombination coefficient in two oppositely moving dipoles. The
key for understanding these unusual properties is that these superlattices have
a unique static electric-field domain. At the same time, their dynamical
behavior is akin to the one of an extended excitable system: an appropriate
finite disturbance of the unique stable fixed point may cause a large excursion
in phase space before returning to the stable state and trigger pulses and wave
trains. The voltage bias constraint causes new waves to be nucleated when old
ones reach the contact.Comment: 19 pages, 8 figures, to appear in Phys. Rev.
Universal behavior in populations composed of excitable and self-oscillatory elements
We study the robustness of self-sustained oscillatory activity in a globally
coupled ensemble of excitable and oscillatory units. The critical balance to
achieve collective self-sustained oscillations is analytically established. We
also report a universal scaling function for the ensemble's mean frequency. Our
results extend the framework of the `Aging Transition' [Phys. Rev. Lett. 93,
104101 (2004)] including a broad class of dynamical systems potentially
relevant in biology.Comment: 4 pages; Changed titl
Vortex Dynamics in Dissipative Systems
We derive the exact equation of motion for a vortex in two- and three-
dimensional non-relativistic systems governed by the Ginzburg-Landau equation
with complex coefficients. The velocity is given in terms of local gradients of
the magnitude and phase of the complex field and is exact also for arbitrarily
small inter-vortex distances. The results for vortices in a superfluid or a
superconductor are recovered.Comment: revtex, 5 pages, 1 encapsulated postscript figure (included), uses
aps.sty, epsf.te
Self-organized transition to coherent activity in disordered media
Synchronized oscillations are of critical functional importance in many
biological systems. We show that such oscillations can arise without
centralized coordination in a disordered system of electrically coupled
excitable and passive cells. Increasing the coupling strength results in waves
that lead to coherent periodic activity, exhibiting cluster, local and global
synchronization under different conditions. Our results may explain the
self-organized transition in a pregnant uterus from transient, localized
activity initially to system-wide coherent excitations just before delivery.Comment: 5 pages, 4 figure
Loss of synchronization in complex neuronal networks with delay
We investigate the stability of synchronization in networks of delay-coupled
excitable neural oscillators. On the basis of the master stability function
formalism, we demonstrate that synchronization is always stable for excitatory
coupling independently of the delay and coupling strength. Superimposing
inhibitory links randomly on top of a regular ring of excitatory coupling,
which yields a small-world-like network topology, we find a phase transition to
desynchronization as the probability of inhibitory links exceeds a critical
value. We explore the scaling of the critical value in dependence on network
properties. Compared to random networks, we find that small-world topologies
are more susceptible to desynchronization via inhibition.Comment: 6 pages, 4 figure
Incorporating Inductances in Tissue-Scale Models of Cardiac Electrophysiology
In standard models of cardiac electrophysiology, including the bidomain and
monodomain models, local perturbations can propagate at infinite speed. We
address this unrealistic property by developing a hyperbolic bidomain model
that is based on a generalization of Ohm's law with a Cattaneo-type model for
the fluxes. Further, we obtain a hyperbolic monodomain model in the case that
the intracellular and extracellular conductivity tensors have the same
anisotropy ratio. In one spatial dimension, the hyperbolic monodomain model is
equivalent to a cable model that includes axial inductances, and the relaxation
times of the Cattaneo fluxes are strictly related to these inductances. A
purely linear analysis shows that the inductances are negligible, but models of
cardiac electrophysiology are highly nonlinear, and linear predictions may not
capture the fully nonlinear dynamics. In fact, contrary to the linear analysis,
we show that for simple nonlinear ionic models, an increase in conduction
velocity is obtained for small and moderate values of the relaxation time. A
similar behavior is also demonstrated with biophysically detailed ionic models.
Using the Fenton-Karma model along with a low-order finite element spatial
discretization, we numerically analyze differences between the standard
monodomain model and the hyperbolic monodomain model. In a simple benchmark
test, we show that the propagation of the action potential is strongly
influenced by the alignment of the fibers with respect to the mesh in both the
parabolic and hyperbolic models when using relatively coarse spatial
discretizations. Accurate predictions of the conduction velocity require
computational mesh spacings on the order of a single cardiac cell. We also
compare the two formulations in the case of spiral break up and atrial
fibrillation in an anatomically detailed model of the left atrium, and [...].Comment: 20 pages, 12 figure
Doppler Effect of Nonlinear Waves and Superspirals in Oscillatory Media
Nonlinear waves emitted from a moving source are studied. A meandering spiral
in a reaction-diffusion medium provides an example, where waves originate from
a source exhibiting a back-and-forth movement in radial direction. The periodic
motion of the source induces a Doppler effect that causes a modulation in
wavelength and amplitude of the waves (``superspiral''). Using the complex
Ginzburg-Landau equation, we show that waves subject to a convective Eckhaus
instability can exhibit monotonous growth or decay as well as saturation of
these modulations away from the source depending on the perturbation frequency.
Our findings allow a consistent interpretation of recent experimental
observations concerning superspirals and their decay to spatio-temporal chaos.Comment: 4 pages, 4 figure
- …