# IX Conference of Young Scientists "Problems of Theoretical Physics"

4-5 December 2018
Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine
Europe/Kiev timezone

## Relation between firing statistics of spiking neuron with delayed feedback and without feedback

4 Dec 2018, 12:25
20m
Oral Statistical Theory of Many-body Systems

### Speaker

Olha Shchur (Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine)

### Description

We consider a class of spiking neuronal models with threshold 2, defined by a set of conditions typical for basic threshold-type models, such as the leaky integrate-and-fire or the binding neuron model and also for some artificial neurons. A neuron is fed with a Poisson process. Each output impulse is applied to the neuron itself after a finite delay $\Delta$. This impulse is identical to those delivered from the input stream. We derive a general relation which allows calculating exactly the probability density function (pdf) $p(t)$ of output interspike intervals of a neuron with feedback based on known pdf $p^0(t)$ for the same neuron without feedback, intensity of the input stream and the properties of the feedback line (the $\Delta$ value).
In addition to this, we calculate exactly the model-independent initial segment of pdf $p(t)$ for a neuron with feedback that is the same for any neuron satisfying the imposed conditions. Also, relations between moments of pdf $p(t)$ for a neuron with feedback and pdf $p^0(t)$ for the same neuron without feedback are derived. The obtained expressions are checked numerically by means of Monte Carlo simulation.
The course of $p(t)$ has a $\delta$-function peculiarity, which makes it impossible to approximate $p(t)$ by Poisson or another simple stochastic process.

### Primary authors

Olha Shchur (Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine) Dr Alexander Vidybida (Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine)

### Presentation Materials

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