873 research outputs found
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
Gap junctions and emergent rhythms
Gap junction coupling is ubiquitous in the brain, particularly between the dendritic trees of inhibitory interneurons. Such direct non-synaptic interaction allows for direct electrical communication between cells. Unlike spike-time driven synaptic neural network models, which are event based, any model with gap junctions must necessarily involve a single neuron model that can represent the shape of an action potential. Indeed, not only do neurons communicating via gaps feel super-threshold spikes, but they also experience, and respond to, sub-threshold voltage signals. In this chapter we show that the so-called absolute integrate-and-fire model is ideally suited to such studies. At the single neuron level voltage traces for the model may be obtained in closed form, and are shown to mimic those of fast-spiking inhibitory neurons. Interestingly in the presence of a slow spike adaptation current the model is shown to support periodic bursting oscillations. For both tonic and bursting modes the phase response curve can be calculated in closed form. At the network level we focus on global gap junction coupling and show how to analyze the asynchronous firing state in large networks. Importantly, we are able to determine the emergence of non-trivial network rhythms due to strong coupling instabilities. To illustrate the use of our theoretical techniques (particularly the phase-density formalism used to determine stability) we focus on a spike adaptation induced transition from asynchronous tonic activity to synchronous bursting in a gap-junction coupled network
Synchronised firing patterns in a random network of adaptive exponential integrate-and-fire neuron model
Acknowledgements This study was possible by partial financial support from the following Brazilian government agencies: CNPq, CAPES, and FAPESP (2011/19296-1 and 2015/07311-7). We also wish thank Newton Fund and COFAP.Peer reviewedPostprin
Within-burst synchrony changes for coupled elliptic bursters
We study the appearance of a novel phenomenon for linearly coupled identical
bursters: synchronized bursts where there are changes of spike synchrony within
each burst. The examples we study are for normal form elliptic bursters where
there is a periodic slow passage through a Bautin (codimension two degenerate
Andronov-Hopf) bifurcation. This burster has a subcritical Andronov-Hopf
bifurcation at the onset of repetitive spiking while end of burst occurs via a
fold limit cycle bifurcation. We study synchronization behavior of two and
three Bautin-type elliptic bursters for a linear direct coupling scheme. Burst
synchronization is known to be prevalent behavior among such coupled bursters,
while spike synchronization is more dependent on the details of the coupling.
We note that higher order terms in the normal form that do not affect the
behavior of a single burster can be responsible for changes in synchrony
pattern; more precisely, we find within-burst synchrony changes associated with
a turning point in the spiking frequency.Comment: 17 pages, 13 figures, 2 table
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