Non-Markovian spiking statistics of a neuron with delayed feedback in presence of refractoriness
Spiking statistics of a self-inhibitory neuron is considered.The neuron receives excitatory input from a Poisson streamand inhibitory impulses through a feedback linewith a delay. After triggering, the neuron is in the refractorystate for a positive period of time. Recently, [...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2013-08-01
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| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.81 |
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| Summary: | Spiking statistics of a self-inhibitory neuron is considered.The neuron receives excitatory input from a Poisson streamand inhibitory impulses through a feedback linewith a delay. After triggering, the neuron is in the refractorystate for a positive period of time. Recently, [35,6], it was proven for a neuron withdelayed feedback and without the refractory state,that the output stream of interspike intervals (ISI)cannot be represented as a Markov process.The refractory state presence, in a sense limits the memory range in thespiking process, which might restore Markov property to the ISI stream. Here we check such a possibility. For this purpose, we calculatethe conditional probability density $P(t_{n+1}\mid t_{n},\ldots,t_1,t_{0})$,and prove exactly that it does not reduce to $P(t_{n+1}\mid t_{n},\ldots,t_1)$for any $n\ge0$. That means, that activity of the system with refractory stateas well cannot be represented as a Markov process of any order. We conclude that it is namely the delayed feedback presencewhich results in non-Markovian statistics of neuronal firing.As delayed feedback lines are common forany realistic neural network, the non-Markovian statistics of the networkactivity should be taken into account in processing of experimental data. |
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| ISSN: | 1551-0018 |