204 research outputs found
Many Attractors, Long Chaotic Transients, and Failure in Small-World Networks of Excitable Neurons
We study the dynamical states that emerge in a small-world network of
recurrently coupled excitable neurons through both numerical and analytical
methods. These dynamics depend in large part on the fraction of long-range
connections or `short-cuts' and the delay in the neuronal interactions.
Persistent activity arises for a small fraction of `short-cuts', while a
transition to failure occurs at a critical value of the `short-cut' density.
The persistent activity consists of multi-stable periodic attractors, the
number of which is at least on the order of the number of neurons in the
network. For long enough delays, network activity at high `short-cut' densities
is shown to exhibit exceedingly long chaotic transients whose failure-times
averaged over many network configurations follow a stretched exponential. We
show how this functional form arises in the ensemble-averaged activity if each
network realization has a characteristic failure-time which is exponentially
distributed.Comment: 14 pages 23 figure
Phase Diffusion in Localized Spatio-Temporal Amplitude Chaos
We present numerical simulations of coupled Ginzburg-Landau equations
describing parametrically excited waves which reveal persistent dynamics due to
the occurrence of phase slips in sequential pairs, with the second phase slip
quickly following and negating the first. Of particular interest are solutions
where these double phase slips occur irregularly in space and time within a
spatially localized region. An effective phase diffusion equation utilizing the
long term phase conservation of the solution explains the localization of this
new form of amplitude chaos.Comment: 4 pages incl. 5 figures uucompresse
Visually induced linear vection is enhanced by small physical accelerations
Wong & Frost (1981) showed that the onset latency of visually induced self-rotation illusions (circular vection) can be reduced by concomitant small physical motions (jerks). Here, we tested whether (a) such facilitation also applies for translations, and (b) whether the strength of the jerk (degree of visuo-vestibular cue conflict) matters. 14 naïve observers rated onset, intensity, and convincingness of forward linear vection induced by photorealistic visual stimuli of a street of houses presented on a projection screen (FOV: 75°×58°). For 2/3 of the trials, brief physical forward accelerations (jerks applied using a Stewart motion platform) accompanied the visual motion onset. Adding jerks enhanced vection significantly; Onset latency was reduced by 50, convincingness and intensity ratings increased by more than 60. Effect size was independent of visual acceleration (1.2 and 12m/s^2) and jerk size (about 0.8 and 1.6m/s^2 at participants’ head for 1 and 3cm displacement, respectively), and showed no interactions. Thus, quantitative matching between the visual and physical acceleration profiles might not be as critical as often believed as long as they match qualitatively and are temporally synchronized. These findings could be employed for improving the convincingness and effectiveness of low-cost simulators without the need for expensive, large motion platforms
Parametric Forcing of Waves with Non-Monotonic Dispersion Relation: Domain Structures in Ferrofluids?
Surface waves on ferrofluids exposed to a dc-magnetic field exhibit a
non-monotonic dispersion relation. The effect of a parametric driving on such
waves is studied within suitable coupled Ginzburg-Landau equations. Due to the
non-monotonicity the neutral curve for the excitation of standing waves can
have up to three minima. The stability of the waves with respect to long-wave
perturbations is determined a phase-diffusion equation. It shows that the
band of stable wave numbers can split up into two or three sub-bands. The
resulting competition between the wave numbers corresponding to the respective
sub-bands leads quite naturally to patterns consisting of multiple domains of
standing waves which differ in their wave number. The coarsening dynamics of
such domain structures is addressed.Comment: 23 pages, 6 postscript figures, composed using RevTeX. Submitted to
PR
Influence of Auditory Cues on the visually-induced Self-Motion Illusion (Circular Vection) in Virtual Reality
This study investigated whether the visually induced selfmotion illusion (“circular vection”) can be enhanced by adding a matching auditory cue (the sound of a fountain that is also visible in the visual stimulus). Twenty observers viewed rotating photorealistic pictures of a market place projected onto a curved projection screen (FOV: 54°x45°). Three conditions were randomized in a repeated measures within-subject design: No sound, mono sound, and spatialized sound using a generic head-related transfer function (HRTF). Adding mono sound increased convincingness ratings marginally, but did not affect any of the other measures of vection or presence. Spatializing the fountain sound, however, improved vection (convincingness and vection buildup time) and presence ratings significantly. Note that facilitation was found even though the visual stimulus was of high quality and realism, and known to be a powerful vection-inducing stimulus. Thus, HRTF-based auralization using headphones can be employed to improve visual VR simulations both in terms of self-motion perception and overall presence
Temporal Modulation of Traveling Waves in the Flow Between Rotating Cylinders With Broken Azimuthal Symmetry
The effect of temporal modulation on traveling waves in the flows in two
distinct systems of rotating cylinders, both with broken azimuthal symmetry,
has been investigated. It is shown that by modulating the control parameter at
twice the critical frequency one can excite phase-locked standing waves and
standing-wave-like states which are not allowed when the system is rotationally
symmetric. We also show how previous theoretical results can be extended to
handle patterns such as these, that are periodic in two spatial direction.Comment: 17 pages in LaTeX, 22 figures available as postscript files from
http://www.esam.nwu.edu/riecke/lit/lit.htm
Domain-size control by global feedback in bistable systems
We study domain structures in bistable systems such as the Ginzburg-Landau
equation. The size of domains can be controlled by a global negative feedback.
The domain-size control is applied for a localized spiral pattern
Defect chaos and bursts: Hexagonal rotating convection and the complex Ginzburg-Landau equation
We employ numerical computations of the full Navier-Stokes equations to investigate non-Boussinesq convection in a rotating system using water as the working fluid. We identify two regimes. For weak non- Boussinesq effects the Hopf bifurcation from steady to oscillating (whirling) hexagons is supercritical and typical states exhibit defect chaos that is systematically described by the cubic complex Ginzburg-Landau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and the oscil- lations exhibit localized chaotic bursting, which is modeled by a quintic complex Ginzburg-Landau equation
Rotating Convection in an Anisotropic System
We study the stability of patterns arising in rotating convection in weakly
anisotropic systems using a modified Swift-Hohenberg equation. The anisotropy,
either an endogenous characteristic of the system or induced by external
forcing, can stabilize periodic rolls in the K\"uppers-Lortz chaotic regime.
For the particular case of rotating convection with time-modulated rotation
where recently, in experiment, chiral patterns have been observed in otherwise
K\"uppers-Lortz-unstable regimes, we show how the underlying base-flow breaks
the isotropy, thereby affecting the linear growth-rate of convection rolls in
such a way as to stabilize spirals and targets. Throughout we compare
analytical results to numerical simulations of the Swift-Hohenberg equation
Whirling Hexagons and Defect Chaos in Hexagonal Non-Boussinesq Convection
We study hexagon patterns in non-Boussinesq convection of a thin rotating
layer of water. For realistic parameters and boundary conditions we identify
various linear instabilities of the pattern. We focus on the dynamics arising
from an oscillatory side-band instability that leads to a spatially disordered
chaotic state characterized by oscillating (whirling) hexagons. Using
triangulation we obtain the distribution functions for the number of pentagonal
and heptagonal convection cells. In contrast to the results found for defect
chaos in the complex Ginzburg-Landau equation and in inclined-layer convection,
the distribution functions can show deviations from a squared Poisson
distribution that suggest non-trivial correlations between the defects.Comment: 4 mpg-movies are available at
http://www.esam.northwestern.edu/~riecke/lit/lit.html submitted to New J.
Physic
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