2,698 research outputs found
Domain wall dynamics in an optical Kerr cavity
An anisotropic (dichroic) optical cavity containing a self-focusing Kerr
medium is shown to display a bifurcation between static --Ising-- and moving
--Bloch-- domain walls, the so-called nonequilibrium Ising-Bloch transition
(NIB). Bloch walls can show regular or irregular temporal behaviour, in
particular, bursting and spiking. These phenomena are interpreted in terms of
the spatio-temporal dynamics of the extended patterns connected by the wall,
which display complex dynamical behaviour as well. Domain wall interaction,
including the formation of bound states is also addressed.Comment: 15 pages Tex file with 11 postscript figures. Resubmitted to Phys.
Rev.
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
Excitability in a nonlinear magnetoacoustic resonator
We report a nonlinear acoustic system displaying excitability. The considered
system is a magnetostrictive material where acoustic waves are parametrically
generated. For a set of parameters, the system presents homoclinic and
heteroclinic dynamics, whose boundaries define a excitability domain. The
excitable behaviour is characterized by analyzing the response of the system to
different external stimuli. Single spiking and bursting regimes have been
identified.Comment: 4 pages, 5 figure
Mechanisms explaining transitions between tonic and phasic firing in neuronal populations as predicted by a low dimensional firing rate model
Several firing patterns experimentally observed in neural populations have
been successfully correlated to animal behavior. Population bursting, hereby
regarded as a period of high firing rate followed by a period of quiescence, is
typically observed in groups of neurons during behavior. Biophysical
membrane-potential models of single cell bursting involve at least three
equations. Extending such models to study the collective behavior of neural
populations involves thousands of equations and can be very expensive
computationally. For this reason, low dimensional population models that
capture biophysical aspects of networks are needed.
\noindent The present paper uses a firing-rate model to study mechanisms that
trigger and stop transitions between tonic and phasic population firing. These
mechanisms are captured through a two-dimensional system, which can potentially
be extended to include interactions between different areas of the nervous
system with a small number of equations. The typical behavior of midbrain
dopaminergic neurons in the rodent is used as an example to illustrate and
interpret our results.
\noindent The model presented here can be used as a building block to study
interactions between networks of neurons. This theoretical approach may help
contextualize and understand the factors involved in regulating burst firing in
populations and how it may modulate distinct aspects of behavior.Comment: 25 pages (including references and appendices); 12 figures uploaded
as separate file
Six Types of Multistability in a Neuronal Model Based on Slow Calcium Current
Background: Multistability of oscillatory and silent regimes is a ubiquitous phenomenon exhibited by excitable systems such as neurons and cardiac cells. Multistability can play functional roles in short-term memory and maintaining posture. It seems to pose an evolutionary advantage for neurons which are part of multifunctional Central Pattern Generators to possess multistability. The mechanisms supporting multistability of bursting regimes are not well understood or classified.
Methodology/Principal Findings: Our study is focused on determining the bio-physical mechanisms underlying different types of co-existence of the oscillatory and silent regimes observed in a neuronal model. We develop a low-dimensional model typifying the dynamics of a single leech heart interneuron. We carry out a bifurcation analysis of the model and show that it possesses six different types of multistability of dynamical regimes. These types are the co-existence of 1) bursting and silence, 2) tonic spiking and silence, 3) tonic spiking and subthreshold oscillations, 4) bursting and subthreshold oscillations, 5) bursting, subthreshold oscillations and silence, and 6) bursting and tonic spiking. These first five types of multistability occur due to the presence of a separating regime that is either a saddle periodic orbit or a saddle equilibrium. We found that the parameter range wherein multistability is observed is limited by the parameter values at which the separating regimes emerge and terminate.
Conclusions: We developed a neuronal model which exhibits a rich variety of different types of multistability. We described a novel mechanism supporting the bistability of bursting and silence. This neuronal model provides a unique opportunity to study the dynamics of networks with neurons possessing different types of multistability
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
Mechanisms of Multistability in Neuronal Models
Multistability is a fundamental attribute of the dynamics of neuronal systems under normal and pathological conditions. The mechanism of bistability of bursting and silence is not well understood and to our knowledge has not been experimentally recorded in single neurons. We considered four models. Two of them described the dynamics of a leech heart interneuron: the canonical model and a low-dimensional model. The other two models described mammalian pacemakers from the respiratory center.
We investigated the low-dimensional model and identified six different types of multistability of dynamical regimes. We described six generic mechanisms underlying the co-existence of oscillatory and silent regimes. The mechanisms are based either on a saddle equilibrium or a saddle periodic orbit. The stable manifold of the saddle equilibrium or the saddle orbit sets the threshold between the regimes. In the two models of the leech interneuron the range of the controlling parameters supporting the co-existence of bursting and silence is limited by the Andronov-Hopf and homoclinic bifurcations (Malashchenko, Master Thesis 2007). The bistability was found in a narrow range of the leak currents\u27 parameters. Here, we introduced a propensity index to bistability as the width of the range on a bifurcation diagram; we investigated how the propensity index was affected by modifications of the ionic currents, and found that conductances of only two currents substantially affected the index. The increase of the conductance of the hyperpolarization-activated current, Ih, and the reduction of the fast Ca2+ current, ICaF, notably increased the propensity index. These findings define modulatory conditions under which we suggest the bistability of bursting and silence could be experimentally revealed in leech heart interneurons. We hypothesize that this mechanism could be commonly found in a large variety of neuronal models. We applied our techniques to models of vertebrate neurons controlling respiratory rhythm, which represent two types of inspiratory pacemakers of the Pre-BÓ§tzinger Complex. We showed that both types of neurons could exhibit bistability of bursting and silence in accordance with the mechanism which we described
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