695 research outputs found
Nonlocal control of pulse propagation in excitable media
We study the effects of nonlocal control of pulse propagation in excitable
media. As a generic example for an excitable medium the FitzHugh-Nagumo model
with diffusion in the activator variable is considered. Nonlocal coupling in
form of an integral term with a spatial kernel is added. We find that the
nonlocal coupling modifies the propagating pulses of the reaction-diffusion
system such that a variety of spatio-temporal patterns are generated including
acceleration, deceleration, suppression, or generation of pulses, multiple
pulses, and blinking pulse trains. It is shown that one can observe these
effects for various choices of the integral kernel and the coupling scheme,
provided that the control strength and spatial extension of the integral kernel
is appropriate. In addition, an analytical procedure is developed to describe
the stability borders of the spatially homogeneous steady state in control
parameter space in dependence on the parameters of the nonlocal coupling
Adaptive synchronization in delay-coupled networks of Stuart-Landau oscillators
We consider networks of delay-coupled Stuart-Landau oscillators. In these
systems, the coupling phase has been found to be a crucial control parameter.
By proper choice of this parameter one can switch between different synchronous
oscillatory states of the network. Applying the speed-gradient method, we
derive an adaptive algorithm for an automatic adjustment of the coupling phase
such that a desired state can be selected from an otherwise multistable regime.
We propose goal functions based on both the difference of the oscillators and a
generalized order parameter and demonstrate that the speed-gradient method
allows one to find appropriate coupling phases with which different states of
synchronization, e.g., in-phase oscillation, splay or various cluster states,
can be selected.Comment: 8 pages, 7 figure
Strain-controlled correlation effects in self-assembled quantum dot stacks
We show that elastic interactions of an array of self-assembled quantum dots
in a parent material matrix are markedly distinct from the elastic field
created by a single point defect, and can explain the observed abrupt
correlation--anticorrelation transition in semiconductor quantum dot stacks.
Finite volume effects of the quantum dots are shown to lead to sharper
transitions. Our analysis also predicts the inclination angle under which the
alignment in successive quantum dot layers occurs in dependence on the material
anisotropy
Nucleation of reaction-diffusion waves on curved surfaces
We study reaction-diffusion waves on curved two-dimensional surfaces, and
determine the influence of curvature upon the nucleation and propagation of
spatially localized waves in an excitable medium modelled by the generic
FitzHugh-Nagumo model. We show that the stability of propagating wave segments
depends crucially on the curvature of the surface. As they propagate, they may
shrink to the uniform steady state, or expand, depending on whether they are
smaller or larger, respectively, than a critical nucleus. This critical nucleus
for wave propagation is modified by the curvature acting like an effective
space-dependent local spatial coupling, similar to diffusion, thus extending
the regime of propagating excitation waves beyond the excitation threshold of
flat surfaces. In particular, a negative gradient of Gaussian curvature
, as on the outside of a torus surface (positive ), when the
wave segment symmetrically extends into the inside (negative ), allows
for stable propagation of localized wave segments remaining unchanged in size
and shape, or oscillating periodically in size
A hybrid model for chaotic front dynamics: From semiconductors to water tanks
We present a general method for studying front propagation in nonlinear
systems with a global constraint in the language of hybrid tank models. The
method is illustrated in the case of semiconductor superlattices, where the
dynamics of the electron accumulation and depletion fronts shows complex
spatio-temporal patterns, including chaos. We show that this behavior may be
elegantly explained by a tank model, for which analytical results on the
emergence of chaos are available. In particular, for the case of three tanks
the bifurcation scenario is characterized by a modified version of the
one-dimensional iterated tent-map.Comment: 4 pages, 4 figure
Controlling surface morphologies by time-delayed feedback
We propose a new method to control the roughness of a growing surface, via a
time-delayed feedback scheme. As an illustration, we apply this method to the
Kardar-Parisi-Zhang equation in 1+1 dimensions and show that the effective
growth exponent of the surface width can be stabilized at any desired value in
the interval [0.25,0.33], for a significant length of time. The method is quite
general and can be applied to a wide range of growth phenomena. A possible
experimental realization is suggested.Comment: 4 pages, 3 figure
Bistable dynamics underlying excitability of ion homeostasis in neuron models
When neurons fire action potentials, dissipation of free energy is usually
not directly considered, because the change in free energy is often negligible
compared to the immense reservoir stored in neural transmembrane ion gradients
and the long-term energy requirements are met through chemical energy, i.e.,
metabolism. However, these gradients can temporarily nearly vanish in
neurological diseases, such as migraine and stroke, and in traumatic brain
injury from concussions to severe injuries. We study biophysical neuron models
based on the Hodgkin-Huxley (HH) formalism extended to include time-dependent
ion concentrations inside and outside the cell and metabolic energy-driven
pumps. We reveal the basic mechanism of a state of free energy-starvation (FES)
with bifurcation analyses showing that ion dynamics is for a large range of
pump rates bistable without contact to an ion bath. This is interpreted as a
threshold reduction of a new fundamental mechanism of 'ionic excitability' that
causes a long-lasting but transient FES as observed in pathological states. We
can in particular conclude that a coupling of extracellular ion concentrations
to a large glial-vascular bath can take a role as an inhibitory mechanism
crucial in ion homeostasis, while the Na/K pumps alone are insufficient
to recover from FES. Our results provide the missing link between the HH
formalism and activator-inhibitor models that have been successfully used for
modeling migraine phenotypes, and therefore will allow us to validate the
hypothesis that migraine symptoms are explained by disturbed function in ion
channel subunits, Na/K pumps, and other proteins that regulate ion
homeostasis.Comment: 14 pages, 8 figures, 4 table
Control of coherence resonance in semiconductor superlattices
We study the effect of time-delayed feedback control and Gaussian white noise
on the spatio-temporal charge dynamics in a semiconductor superlattice. The
system is prepared in a regime where the deterministic dynamics is close to a
global bifurcation, namely a saddle-node bifurcation on a limit cycle ({\it
SNIPER}). In the absence of control, noise can induce electron charge front
motion through the entire device, and coherence resonance is observed. We show
that with appropriate selection of the time-delayed feedback parameters the
effect of coherence resonance can either be enhanced or destroyed, and the
coherence of stochastic domain motion at low noise intensity is dramatically
increased. Additionally, the purely delay-induced dynamics in the system is
investigated, and a homoclinic bifurcation of a limit cycle is found.Comment: 7 pages, 7 figure
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