788 research outputs found
Model of the early development of thalamo-cortical connections and area patterning via signaling molecules
The mammalian cortex is divided into architectonic and functionally distinct
areas. There is growing experimental evidence that their emergence and
development is controlled by both epigenetic and genetic factors. The latter
were recently implicated as dominating the early cortical area specification.
In this paper, we present a theoretical model that explicitly considers the
genetic factors and that is able to explain several sets of experiments on
cortical area regulation involving transcription factors Emx2 and Pax6, and
fibroblast growth factor FGF8. The model consists of the dynamics of thalamo-
cortical connections modulated by signaling molecules that are regulated
genetically, and by axonal competition for neocortical space. The model can
make predictions and provides a basic mathematical framework for the early
development of the thalamo-cortical connections and area patterning that can be
further refined as more experimental facts become known.Comment: brain, model, neural development, cortical area patterning, signaling
molecule
Formation of antiwaves in gap-junction-coupled chains of neurons
Using network models consisting of gap junction coupled Wang-Buszaki neurons,
we demonstrate that it is possible to obtain not only synchronous activity
between neurons but also a variety of constant phase shifts between 0 and \pi.
We call these phase shifts intermediate stable phaselocked states. These phase
shifts can produce a large variety of wave-like activity patterns in
one-dimensional chains and two-dimensional arrays of neurons, which can be
studied by reducing the system of equations to a phase model. The 2\pi periodic
coupling functions of these models are characterized by prominent higher order
terms in their Fourier expansion, which can be varied by changing model
parameters. We study how the relative contribution of the odd and even terms
affect what solutions are possible, the basin of attraction of those solutions
and their stability. These models may be applicable to the spinal central
pattern generators of the dogfish and also to the developing neocortex of the
neonatal rat
Renewal theory of coupled neuronal pools
A theory is provided to analyze the dynamics of delay-coupled pools of spiking neurons based on stability
analysis of stationary firing. Transitions between stable and unstable regimes can be predicted by bifurcation analysis of the underlying integral dynamics. Close to the bifurcation point the network exhibits slowly changingactivities and allows for slow collective phenomena like continuous attractors
Chimera States for Coupled Oscillators
Arrays of identical oscillators can display a remarkable spatiotemporal
pattern in which phase-locked oscillators coexist with drifting ones.
Discovered two years ago, such "chimera states" are believed to be impossible
for locally or globally coupled systems; they are peculiar to the intermediate
case of nonlocal coupling. Here we present an exact solution for this state,
for a ring of phase oscillators coupled by a cosine kernel. We show that the
stable chimera state bifurcates from a spatially modulated drift state, and
dies in a saddle-node bifurcation with an unstable chimera.Comment: 4 pages, 4 figure
Phase Response Curves of Coupled Oscillators
Many real oscillators are coupled to other oscillators and the coupling can
affect the response of the oscillators to stimuli. We investigate phase
response curves (PRCs) of coupled oscillators. The PRCs for two weakly coupled
phase-locked oscillators are analytically obtained in terms of the PRC for
uncoupled oscillators and the coupling function of the system. Through
simulation and analytic methods, the PRCs for globally coupled oscillators are
also discussed.Comment: 5 pages 4 figur
Synchronization Transition in the Kuramoto Model with Colored Noise
We present a linear stability analysis of the incoherent state in a system of
globally coupled, identical phase oscillators subject to colored noise. In that
we succeed to bridge the extreme time scales between the formerly studied and
analytically solvable cases of white noise and quenched random frequencies.Comment: 4 pages, 2 figure
Clustered chimera states in delay coupled oscillator systems
We investigate "chimera" states in a ring of identical phase oscillators
coupled in a time-delayed and spatially non-local fashion. We find novel
"clustered chimera" states that have spatially distributed phase coherence
separated by incoherence with adjacent coherent regions in anti-phase. The
existence of such time-delay induced phase clustering is further supported
through solutions of a generalized functional self-consistency equation of the
mean field. Our results highlight an additional mechanism for cluster formation
that may find wider practical applications
Effective phase description of noise-perturbed and noise-induced oscillations
An effective description of a general class of stochastic phase oscillators
is presented. For this, the effective phase velocity is defined either by
invariant probability density or via first passage times. While the first
approach exhibits correct frequency and distribution density, the second one
yields proper phase resetting curves. Their discrepancy is most pronounced for
noise-induced oscillations and is related to non-monotonicity of the phase
fluctuations
Limits and dynamics of stochastic neuronal networks with random heterogeneous delays
Realistic networks display heterogeneous transmission delays. We analyze here
the limits of large stochastic multi-populations networks with stochastic
coupling and random interconnection delays. We show that depending on the
nature of the delays distributions, a quenched or averaged propagation of chaos
takes place in these networks, and that the network equations converge towards
a delayed McKean-Vlasov equation with distributed delays. Our approach is
mostly fitted to neuroscience applications. We instantiate in particular a
classical neuronal model, the Wilson and Cowan system, and show that the
obtained limit equations have Gaussian solutions whose mean and standard
deviation satisfy a closed set of coupled delay differential equations in which
the distribution of delays and the noise levels appear as parameters. This
allows to uncover precisely the effects of noise, delays and coupling on the
dynamics of such heterogeneous networks, in particular their role in the
emergence of synchronized oscillations. We show in several examples that not
only the averaged delay, but also the dispersion, govern the dynamics of such
networks.Comment: Corrected misprint (useless stopping time) in proof of Lemma 1 and
clarified a regularity hypothesis (remark 1
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