4,484 research outputs found
Phase-locking in weakly heterogeneous neuronal networks
We examine analytically the existence and stability of phase-locked states in
a weakly heterogeneous neuronal network. We consider a model of N neurons with
all-to-all synaptic coupling where the heterogeneity is in the firing frequency
or intrinsic drive of the neurons. We consider both inhibitory and excitatory
coupling. We derive the conditions under which stable phase-locking is
possible. In homogeneous networks, many different periodic phase-locked states
are possible. Their stability depends on the dynamics of the neuron and the
coupling. For weak heterogeneity, the phase-locked states are perturbed from
the homogeneous states and can remain stable if their homogeneous conterparts
are stable. For enough heterogeneity, phase-locked solutions either lose
stability or are destroyed completely. We analyze the possible states the
network can take when phase-locking is broken.Comment: RevTex, 27 pages, 3 figure
Synchronization of electrically coupled resonate-and-fire neurons
Electrical coupling between neurons is broadly present across brain areas and
is typically assumed to synchronize network activity. However, intrinsic
properties of the coupled cells can complicate this simple picture. Many cell
types with strong electrical coupling have been shown to exhibit resonant
properties, and the subthreshold fluctuations arising from resonance are
transmitted through electrical synapses in addition to action potentials. Using
the theory of weakly coupled oscillators, we explore the effect of both
subthreshold and spike-mediated coupling on synchrony in small networks of
electrically coupled resonate-and-fire neurons, a hybrid neuron model with
linear subthreshold dynamics and discrete post-spike reset. We calculate the
phase response curve using an extension of the adjoint method that accounts for
the discontinuity in the dynamics. We find that both spikes and resonant
subthreshold fluctuations can jointly promote synchronization. The subthreshold
contribution is strongest when the voltage exhibits a significant post-spike
elevation in voltage, or plateau. Additionally, we show that the geometry of
trajectories approaching the spiking threshold causes a "reset-induced shear"
effect that can oppose synchrony in the presence of network asymmetry, despite
having no effect on the phase-locking of symmetrically coupled pairs
One-Dimensional Population Density Approaches to Recurrently Coupled Networks of Neurons with Noise
Mean-field systems have been previously derived for networks of coupled,
two-dimensional, integrate-and-fire neurons such as the Izhikevich, adapting
exponential (AdEx) and quartic integrate and fire (QIF), among others.
Unfortunately, the mean-field systems have a degree of frequency error and the
networks analyzed often do not include noise when there is adaptation. Here, we
derive a one-dimensional partial differential equation (PDE) approximation for
the marginal voltage density under a first order moment closure for coupled
networks of integrate-and-fire neurons with white noise inputs. The PDE has
substantially less frequency error than the mean-field system, and provides a
great deal more information, at the cost of analytical tractability. The
convergence properties of the mean-field system in the low noise limit are
elucidated. A novel method for the analysis of the stability of the
asynchronous tonic firing solution is also presented and implemented. Unlike
previous attempts at stability analysis with these network types, information
about the marginal densities of the adaptation variables is used. This method
can in principle be applied to other systems with nonlinear partial
differential equations.Comment: 26 Pages, 6 Figure
Internetwork and intranetwork communications during bursting dynamics: Applications to seizure prediction
We use a simple dynamical model of two interacting networks of integrate-and-fire neurons to explain a seemingly paradoxical result observed in epileptic patients indicating that the level of phase synchrony declines below normal levels during the state preceding seizures (preictal state). We model the transition from the seizure free interval (interictal state) to the seizure (ictal state) as a slow increase in the mean depolarization of neurons in a network corresponding to the epileptic focus. We show that the transition from the interictal to preictal and then to the ictal state may be divided into separate dynamical regimes: the formation of slow oscillatory activity due to resonance between the two interacting networks observed during the interictal period, structureless activity during the preictal period when the two networks have different properties, and bursting dynamics driven by the network corresponding to the epileptic focus. Based on this result, we hypothesize that the beginning of the preictal period marks the beginning of the transition of the epileptic network from normal activity toward seizing
Temporal album
Transient synchronization has been used as a mechanism of recognizing auditory patterns using integrate-and-fire neural networks. We first extend the mechanism to vision tasks and investigate the role of spike dependent learning. We show that such a temporal Hebbian learning rule significantly improves accuracy of detection. We demonstrate how multiple patterns can be identified by a single pattern selective neuron and how a temporal album can be constructed. This principle may lead to multidimensional memories, where the capacity per neuron is considerably increased with accurate detection of spike synchronization
Inhibitory synchrony as a mechanism for attentional gain modulation
Recordings from area V4 of monkeys have revealed that when the focus of
attention is on a visual stimulus within the receptive field of a cortical
neuron, two distinct changes can occur: The firing rate of the neuron can
change and there can be an increase in the coherence between spikes and the
local field potential in the gamma-frequency range (30-50 Hz). The hypothesis
explored here is that these observed effects of attention could be a
consequence of changes in the synchrony of local interneuron networks. We
performed computer simulations of a Hodgkin-Huxley type neuron driven by a
constant depolarizing current, I, representing visual stimulation and a
modulatory inhibitory input representing the effects of attention via local
interneuron networks. We observed that the neuron's firing rate and the
coherence of its output spike train with the synaptic inputs was modulated by
the degree of synchrony of the inhibitory inputs. The model suggest that the
observed changes in firing rate and coherence of neurons in the visual cortex
could be controlled by top-down inputs that regulated the coherence in the
activity of a local inhibitory network discharging at gamma frequencies.Comment: J.Physiology (Paris) in press, 11 figure
Conedy: a scientific tool to investigate Complex Network Dynamics
We present Conedy, a performant scientific tool to numerically investigate
dynamics on complex networks. Conedy allows to create networks and provides
automatic code generation and compilation to ensure performant treatment of
arbitrary node dynamics. Conedy can be interfaced via an internal script
interpreter or via a Python module
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