The stochastic, Markovian, Hodgkin-Huxley type of mathematical model of the neuron

Aleksandra Świetlicka, Karol Gugała, Agata Jurkowlaniec, Pawel Śniatała, Andrzej Rybarczyk


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 implemen- tation 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.


Hodgkin-Huxley model; stochastic differential equations; Markov kinetics; kinetic formalism; field-programmable gate array (FPGA)

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