Fast {\large\it Cl-}type inhibitory neuron with delayed feedback has non-markov output statistics

TL;DR

This paper proves that certain fast Cl- type inhibitory neurons with delayed feedback produce output spike intervals that cannot be modeled as Markov processes, highlighting complex temporal dynamics.

Contribution

It introduces a proof that the output of specific inhibitory neuron models with delayed feedback defies Markovian description, advancing understanding of neural spike train statistics.

Findings

Output interspike intervals are non-Markovian for the studied neuron models.

Delayed feedback induces complex, non-Markovian spike timing.

The result applies to neurons driven by Poisson input.

Abstract

For a class of fast {\it Cl-}type inhibitory spiking neuron models with delayed feedback fed with a Poisson stochastic process of excitatory impulses, it is proven that the stream of output interspike intervals cannot be presented as a Markov process of any order.