351 research outputs found
Modeling of Spiking-Bursting Neural Behavior Using Two-Dimensional Map
A simple model that replicates the dynamics of spiking and spiking-bursting
activity of real biological neurons is proposed. The model is a two-dimensional
map which contains one fast and one slow variable. The mechanisms behind
generation of spikes, bursts of spikes, and restructuring of the map behavior
are explained using phase portrait analysis. The dynamics of two coupled maps
which model the behavior of two electrically coupled neurons is discussed.
Synchronization regimes for spiking and bursting activity of these maps are
studied as a function of coupling strength. It is demonstrated that the results
of this model are in agreement with the synchronization of chaotic
spiking-bursting behavior experimentally found in real biological neurons.Comment: 9 pages, 12 figure
Demarcating the Right to Gather News: A Sequential Interpretation of the First Amendment
In this paper we construct well-posed boundary conditions for the compressible Euler and Navier-Stokes equations in two space dimensions. When also considering the dual equations, we show how to construct the boundary conditions so that both the primal and dual problems are well-posed. By considering the primal and dual problems simultaneously, we construct energy stable and dual consistent finite difference schemes on summation-by-Â parts form with weak imposition of the boundary conditions. According to linear theory, the stable and dual consistent discretization can be used to compute linear integral functionals from the solution at a superconvergent rate. Here we evaluate numerically the superconvergence property for the non-linear Euler and Navier{ Stokes equations with linear and non-linear integral functionals
New way to achieve chaotic synchronization in spatially extended systems
We study the spatio-temporal behavior of simple coupled map lattices with
periodic boundary conditions. The local dynamics is governed by two maps,
namely, the sine circle map and the logistic map respectively. It is found that
even though the spatial behavior is irregular for the regularly coupled
(nearest neighbor coupling) system, the spatially synchronized (chaotic
synchronization) as well as periodic solution may be obtained by the
introduction of three long range couplings at the cost of three nearest
neighbor couplings.Comment: 5 pages (revtex), 7 figures (eps, included
Using Synchronization for Prediction of High-Dimensional Chaotic Dynamics
We experimentally observe the nonlinear dynamics of an optoelectronic
time-delayed feedback loop designed for chaotic communication using commercial
fiber optic links, and we simulate the system using delay differential
equations. We show that synchronization of a numerical model to experimental
measurements provides a new way to assimilate data and forecast the future of
this time-delayed high-dimensional system. For this system, which has a
feedback time delay of 22 ns, we show that one can predict the time series for
up to several delay periods, when the dynamics is about 15 dimensional.Comment: 10 pages, 4 figure
Magnetic-film atom chip with 10 m period lattices of microtraps for quantum information science with Rydberg atoms
We describe the fabrication and construction of a setup for creating lattices
of magnetic microtraps for ultracold atoms on an atom chip. The lattice is
defined by lithographic patterning of a permanent magnetic film. Patterned
magnetic-film atom chips enable a large variety of trapping geometries over a
wide range of length scales. We demonstrate an atom chip with a lattice
constant of 10 m, suitable for experiments in quantum information science
employing the interaction between atoms in highly-excited Rydberg energy
levels. The active trapping region contains lattice regions with square and
hexagonal symmetry, with the two regions joined at an interface. A structure of
macroscopic wires, cut out of a silver foil, was mounted under the atom chip in
order to load ultracold Rb atoms into the microtraps. We demonstrate
loading of atoms into the square and hexagonal lattice sections simultaneously
and show resolved imaging of individual lattice sites. Magnetic-film lattices
on atom chips provide a versatile platform for experiments with ultracold
atoms, in particular for quantum information science and quantum simulation.Comment: 7 pages, 7 figure
Topological signature of deterministic chaos in short nonstationary signals from an optical parametric oscillator
Although deterministic chaos has been predicted to occur in the triply
resonant optical parametric oscillator (TROPO) fifteen years ago, experimental
evidence of chaotic behavior in this system has been lacking so far, in marked
contrast with most nonlinear systems, where chaos has been actively tracked and
found. This situation is probably linked to the high sensitivity of the TROPO
to perturbations, which adversely affects stationary operation at high power.
We report the experimental observation in this system of a burst of irregular
behavior of duration 80 microseconds. Although the system is highly
nonstationary over this time interval, a topological analysis allows us to
extract a clearcut signature of deterministic chaos from a time series segment
of only 9 base cycles (3 microseconds). This result suggests that
nonstationarity is not necessarily an obstacle to the characterization of
chaos
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