25,668 research outputs found
Introduction: Localized Structures in Dissipative Media: From Optics to Plant Ecology
Localised structures in dissipative appears in various fields of natural
science such as biology, chemistry, plant ecology, optics and laser physics.
The proposed theme issue is to gather specialists from various fields of
non-linear science toward a cross-fertilisation among active areas of research.
This is a cross-disciplinary area of research dominated by the nonlinear optics
due to potential applications for all-optical control of light, optical
storage, and information processing. This theme issue contains contributions
from 18 active groups involved in localized structures field and have all made
significant contributions in recent years.Comment: 14 pages, 0 figure, submitted to Phi. Trasaction Royal Societ
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
Arrest of Domain Coarsening via Antiperiodic Regimes in Delay Systems
Motionless domains walls representing heteroclinic temporal or spatial orbits
typically exist only for very specific parameters. This report introduces a
novel mechanism for stabilizing temporal domain walls away from the Maxwell
point opening up new possibilities to encode information in dynamical systems.
It is based on anti-periodic regimes in a delayed system close to a bistable
situation, leading to a cancellation of the average drift velocity. The results
are demonstrated in a normal form model and experimentally in a laser with
optical injection and delayed feedback.Comment: 6 pages, 5 figures, resubmitted manuscrip
Symmetry Groupoids for Pattern-Selective Feedback Stabilization of the Chafee--Infante Equation
Reaction-diffusion equations are ubiquitous in various scientific domains and
their patterns represent a fascinating area of investigation. However, many of
these patterns are unstable and therefore challenging to observe. To overcome
this limitation, we present new noninvasive feedback controls based on symmetry
groupoids. As a concrete example, we employ these controls to selectively
stabilize unstable equilibria of the Chafee--Infante equation under Dirichlet
boundary conditions on the interval. Unlike conventional reflection-based
control schemes, our approach incorporates additional symmetries that enable us
to design new convolution controls for stabilization. By demonstrating the
efficacy of our method, we provide a new tool for investigating and controlling
systems with unstable patterns, with potential implications for a wide range of
scientific disciplines
Temporal Dynamics of Decision-Making during Motion Perception in the Visual Cortex
How does the brain make decisions? Speed and accuracy of perceptual decisions covary with certainty in the input, and correlate with the rate of evidence accumulation in parietal and frontal cortical "decision neurons." A biophysically realistic model of interactions within and between Retina/LGN and cortical areas V1, MT, MST, and LIP, gated by basal ganglia, simulates dynamic properties of decision-making in response to ambiguous visual motion stimuli used by Newsome, Shadlen, and colleagues in their neurophysiological experiments. The model clarifies how brain circuits that solve the aperture problem interact with a recurrent competitive network with self-normalizing choice properties to carry out probablistic decisions in real time. Some scientists claim that perception and decision-making can be described using Bayesian inference or related general statistical ideas, that estimate the optimal interpretation of the stimulus given priors and likelihoods. However, such concepts do not propose the neocortical mechanisms that enable perception, and make decisions. The present model explains behavioral and neurophysiological decision-making data without an appeal to Bayesian concepts and, unlike other existing models of these data, generates perceptual representations and choice dynamics in response to the experimental visual stimuli. Quantitative model simulations include the time course of LIP neuronal dynamics, as well as behavioral accuracy and reaction time properties, during both correct and error trials at different levels of input ambiguity in both fixed duration and reaction time tasks. Model MT/MST interactions compute the global direction of random dot motion stimuli, while model LIP computes the stochastic perceptual decision that leads to a saccadic eye movement.National Science Foundation (SBE-0354378, IIS-02-05271); Office of Naval Research (N00014-01-1-0624); National Institutes of Health (R01-DC-02852
Two-dimensional wave patterns of spreading depolarization: retracting, re-entrant, and stationary waves
We present spatio-temporal characteristics of spreading depolarizations (SD)
in two experimental systems: retracting SD wave segments observed with
intrinsic optical signals in chicken retina, and spontaneously occurring
re-entrant SD waves that repeatedly spread across gyrencephalic feline cortex
observed by laser speckle flowmetry. A mathematical framework of
reaction-diffusion systems with augmented transmission capabilities is
developed to explain the emergence and transitions between these patterns. Our
prediction is that the observed patterns are reaction-diffusion patterns
controlled and modulated by weak nonlocal coupling. The described
spatio-temporal characteristics of SD are of important clinical relevance under
conditions of migraine and stroke. In stroke, the emergence of re-entrant SD
waves is believed to worsen outcome. In migraine, retracting SD wave segments
cause neurological symptoms and transitions to stationary SD wave patterns may
cause persistent symptoms without evidence from noninvasive imaging of
infarction
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