500 research outputs found
Chaos at the border of criticality
The present paper points out to a novel scenario for formation of chaotic
attractors in a class of models of excitable cell membranes near an
Andronov-Hopf bifurcation (AHB). The mechanism underlying chaotic dynamics
admits a simple and visual description in terms of the families of
one-dimensional first-return maps, which are constructed using the combination
of asymptotic and numerical techniques. The bifurcation structure of the
continuous system (specifically, the proximity to a degenerate AHB) endows the
Poincare map with distinct qualitative features such as unimodality and the
presence of the boundary layer, where the map is strongly expanding. This
structure of the map in turn explains the bifurcation scenarios in the
continuous system including chaotic mixed-mode oscillations near the border
between the regions of sub- and supercritical AHB. The proposed mechanism
yields the statistical properties of the mixed-mode oscillations in this
regime. The statistics predicted by the analysis of the Poincare map and those
observed in the numerical experiments of the continuous system show a very good
agreement.Comment: Chaos: An Interdisciplinary Journal of Nonlinear Science
(tentatively, Sept 2008
Autonomous Bursting in a Homoclinic System
A continuous train of irregularly spaced spikes, peculiar of homoclinic
chaos, transforms into clusters of regularly spaced spikes, with quiescent
periods in between (bursting regime), by feeding back a low frequency portion
of the dynamical output. Such autonomous bursting results to be extremely
robust against noise; we provide experimental evidence of it in a CO2 laser
with feedback. The phenomen here presented display qualitative analogies with
bursting phenomena in neurons.Comment: Submitted to Phys. Rev. Lett., 14 pages, 5 figure
Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons
The dynamics of two coupled piece-wise linear one-dimensional monostable maps
is investigated. The single map is associated with Poincare section of the
FitzHugh-Nagumo neuron model. It is found that a diffusive coupling leads to
the appearance of chaotic attractor. The attractor exists in an invariant
region of phase space bounded by the manifolds of the saddle fixed point and
the saddle periodic point. The oscillations from the chaotic attractor have a
spike-burst shape with anti-phase synchronized spiking.Comment: To be published in CHAO
Dynamics of excitable cells: spike-adding phenomena in action
We study the dynamics of action potentials of some electrically excitable cells: neurons and cardiac muscle cells. Bursting, following a fastâslow dynamics, is the most characteristic behavior of these dynamical systems, and the number of spikes may change due to spike-adding phenomenon. Using analytical and numerical methods we give, by focusing on the paradigmatic 3D HindmarshâRose neuron model, a review of recent results on the global organization of the parameter space of neuron models with bursting regions occurring between saddle-node and homoclinic bifurcations (fold/hom bursting). We provide a generic overview of the different bursting regimes that appear in the parametric phase space of the model and the bifurcations among them. These techniques are applied in two realistic frameworks: insect movement gait changes and the appearance of Early Afterdepolarizations in cardiac dynamics
Mechanism, dynamics, and biological existence of multistability in a large class of bursting neurons
Multistability, the coexistence of multiple attractors in a dynamical system,
is explored in bursting nerve cells. A modeling study is performed to show that
a large class of bursting systems, as defined by a shared topology when
represented as dynamical systems, is inherently suited to support
multistability. We derive the bifurcation structure and parametric trends
leading to multistability in these systems. Evidence for the existence of
multirhythmic behavior in neurons of the aquatic mollusc Aplysia californica
that is consistent with our proposed mechanism is presented. Although these
experimental results are preliminary, they indicate that single neurons may be
capable of dynamically storing information for longer time scales than
typically attributed to nonsynaptic mechanisms.Comment: 24 pages, 8 figure
Chaotic oscillations in a map-based model of neural activity
We propose a discrete time dynamical system (a map) as phenomenological model
of excitable and spiking-bursting neurons. The model is a discontinuous
two-dimensional map. We find condition under which this map has an invariant
region on the phase plane, containing chaotic attractor. This attractor creates
chaotic spiking-bursting oscillations of the model. We also show various
regimes of other neural activities (subthreshold oscillations, phasic spiking
etc.) derived from the proposed model
A comparative study fourth order runge kutta-tvd Scheme and fluent software case of inlet flow problems
Inlet as part of aircraft engine plays important role in controlling the rate of airflow
entering to the engine. The shape of inlet has to be designed in such away to make the
rate of airflow does not change too much with angle of attack and also not much
pressure losses at the time, the airflow entering to the compressor section. It is therefore
understanding on the flow pattern inside the inlet is important. The present work
presents on the use of the Fourth Order Runge Kutta â Harten Yee TVD scheme
for
the flow analysis inside inlet. The flow is assumed as an inviscid quasi two dimensional
compressible flow. As an initial stage of computer code development, here uses three
generic inlet models. The first inlet model to allow the problem in hand solved as the
case of inlet with expansion wave case. The second inlet model will relate to the case of
expansion compression wave. The last inlet model concerns with the inlet which
produce series of weak shock wave and end up with a normal shock wave. The
comparison result for the same test case with Fluent Software
[1, 2]
indicates that the
developed computer code based on the Fourth Order Runge Kutta â Harten â Yee TVD
scheme are very close to each other. However for complex inlet geometry, the problem
is in the way how to provide an appropriate mesh model
Spontaneous spiking in an autaptic Hodgkin-Huxley set up
The effect of intrinsic channel noise is investigated for the dynamic
response of a neuronal cell with a delayed feedback loop. The loop is based on
the so-called autapse phenomenon in which dendrites establish not only
connections to neighboring cells but as well to its own axon. The biophysical
modeling is achieved in terms of a stochastic Hodgkin-Huxley model containing
such a built in delayed feedback. The fluctuations stem from intrinsic channel
noise, being caused by the stochastic nature of the gating dynamics of ion
channels. The influence of the delayed stimulus is systematically analyzed with
respect to the coupling parameter and the delay time in terms of the interspike
interval histograms and the average interspike interval. The delayed feedback
manifests itself in the occurrence of bursting and a rich multimodal interspike
interval distribution, exhibiting a delay-induced reduction of the spontaneous
spiking activity at characteristic frequencies. Moreover, a specific
frequency-locking mechanism is detected for the mean interspike interval.Comment: 8 pages, 10 figure
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