10,496 research outputs found
Average activity of excitatory and inhibitory neural populations
We develop an extension of the Ott-Antonsen method [E. Ott and T. M. Antonsen, Chaos 18(3), 037113 (2008)] that allows obtaining the mean activity (spiking rate) of a population of excitable units. By means of the Ott-Antonsen method, equations for the dynamics of the order parameters of coupled excitatory and inhibitory populations of excitable units are obtained, and their mean activities are computed. Two different excitable systems are studied: Adler units and theta neurons. The resulting bifurcation diagrams are compared with those obtained from studying the phenomenological Wilson-Cowan model in some regions of the parameter space. Compatible behaviors, as well as higher dimensional chaotic solutions, are observed. We study numerical simulations to further validate the equations.Fil: Roulet, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Mindlin, Bernardo Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentin
Stability diagrams for bursting neurons modeled by three-variable maps
We study a simple map as a minimal model of excitable cells. The map has two
fast variables which mimic the behavior of class I neurons, undergoing a
sub-critical Hopf bifurcation. Adding a third slow variable allows the system
to present bursts and other interesting biological behaviors. Bifurcation lines
which locate the excitability region are obtained for different planes in
parameter space.Comment: 7 pages, 3 figures, accepted for publicatio
Dynamical laser spike processing
Novel materials and devices in photonics have the potential to revolutionize
optical information processing, beyond conventional binary-logic approaches.
Laser systems offer a rich repertoire of useful dynamical behaviors, including
the excitable dynamics also found in the time-resolved "spiking" of neurons.
Spiking reconciles the expressiveness and efficiency of analog processing with
the robustness and scalability of digital processing. We demonstrate that
graphene-coupled laser systems offer a unified low-level spike optical
processing paradigm that goes well beyond previously studied laser dynamics. We
show that this platform can simultaneously exhibit logic-level restoration,
cascadability and input-output isolation---fundamental challenges in optical
information processing. We also implement low-level spike-processing tasks that
are critical for higher level processing: temporal pattern detection and stable
recurrent memory. We study these properties in the context of a fiber laser
system, but the addition of graphene leads to a number of advantages which stem
from its unique properties, including high absorption and fast carrier
relaxation. These could lead to significant speed and efficiency improvements
in unconventional laser processing devices, and ongoing research on graphene
microfabrication promises compatibility with integrated laser platforms.Comment: 13 pages, 7 figure
Critical phenomena in globally coupled excitable elements
Critical phenomena in globally coupled excitable elements are studied by
focusing on a saddle-node bifurcation at the collective level. Critical
exponents that characterize divergent fluctuations of interspike intervals near
the bifurcation are calculated theoretically. The calculated values appear to
be in good agreement with those determined by numerical experiments. The
relevance of our results to jamming transitions is also mentioned.Comment: 4 pages, 3 figure
Multiscale modeling of oscillations and spiral waves in Dictyostelium populations
Unicellular organisms exhibit elaborate collective behaviors in response to
environmental cues. These behaviors are controlled by complex biochemical
networks within individual cells and coordinated through cell-to-cell
communication. Describing these behaviors requires new mathematical models that
can bridge scales -- from biochemical networks within individual cells to
spatially structured cellular populations. Here, we present a family of
multiscale models for the emergence of spiral waves in the social amoeba
Dictyostelium discoideum. Our models exploit new experimental advances that
allow for the direct measurement and manipulation of the small signaling
molecule cAMP used by Dictyostelium cells to coordinate behavior in cellular
populations. Inspired by recent experiments, we model the Dictyostelium
signaling network as an excitable system coupled to various pre-processing
modules. We use this family of models to study spatially unstructured
populations by constructing phase diagrams that relate the properties of
population-level oscillations to parameters in the underlying biochemical
network. We then extend our models to include spatial structure and show how
they naturally give rise to spiral waves. Our models exhibit a wide range of
novel phenomena including a density dependent frequency change, bistability,
and dynamic death due to slow cAMP dynamics. Our modeling approach provides a
powerful tool for bridging scales in modeling of Dictyostelium populations
Effects of a localized beam on the dynamics of excitable cavity solitons
We study the dynamical behavior of dissipative solitons in an optical cavity
filled with a Kerr medium when a localized beam is applied on top of the
homogeneous pumping. In particular, we report on the excitability regime that
cavity solitons exhibits which is emergent property since the system is not
locally excitable. The resulting scenario differs in an important way from the
case of a purely homogeneous pump and now two different excitable regimes, both
Class I, are shown. The whole scenario is presented and discussed, showing that
it is organized by three codimension-2 points. Moreover, the localized beam can
be used to control important features, such as the excitable threshold,
improving the possibilities for the experimental observation of this
phenomenon.Comment: 9 Pages, 12 figure
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