THE STOCHASTIC, MARKOVIAN, HODGKIN-HUXLEY TYPE OF MATHEMATICAL MODEL OF THE NEURON

The aim of this paper is to show how the Hodgkin-Huxley model of the neuron's membrane potential can be extended to a stochastic one. This extension can be done either by adding fluctuations to the equations of the model or by using Markov kinetic schemes' formalism. We are presenting a ne...

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Published inNeural Network World Vol. 25; no. 3; pp. 219 - 239
Main Authors Świetlicka, Aleksandra, Gugała, Karol, Jurkowlaniec, Agata, Śniatała, Pawel, Rybarczyk, Andrzej
Format Journal Article
LanguageEnglish
Published Prague Institute of Information and Computer Technology 01.01.2015
Czech Technical University in Prague, Faculty of Transportation Sciences
Subjects
Field programmable gate arrays
Formalism
Hardware
Markov analysis
Markov models
Mathematical models
Neural networks
Neurons
Stochastic models
Stochasticity
kinetic formalism
Hodgkin-Huxley model
stochastic differential equations
field-programmable gate array (FPGA)
Markov kinetics
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Summary:The aim of this paper is to show how the Hodgkin-Huxley model of the neuron's membrane potential can be extended to a stochastic one. This extension can be done either by adding fluctuations to the equations of the model or by using Markov kinetic schemes' formalism. We are presenting a new extension of the model. This modification simplifies computational complexity of the neuron model especially when considering a hardware implementation. The hardware implementation of the extended model as a system on a chip using a field-programmable gate array (FPGA) is demonstrated in this paper. The results confirm the reliability of the extended model presented here.
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ISSN:1210-0552
2336-4335
DOI:10.14311/NNW.2015.25.012