Razali, Nur Shafika Abel
(2019)
Dynamical System Study Of The Hodgkin-Huxley, Fitzhugh-Nagumo And Morris-Lecar Models Of Nerve Membranes.
PhD thesis, Universiti Sains Malaysia.
Abstract
The mechanism of signals transmitting in a single neuron has been modelled
in mathematical neuroscience since the past few decades. One of the well-known
mathematical neuronal models is the Hodgkin-Huxley (HH) model that models the
dynamics of ionic channels embedded along the axon. When parameter values are
varied, the HH model can show a variety of different qualitative behaviours. This
means that the nervous system has been altered and this might relate to some
neuronal diseases. New medical diagnosis can be made by bringing the parameter
values back to its reasonable range. Thus, it is very important to analyse the
dynamical systems of a single neuron model in one- and two-parameters bifurcation
diagrams, and to study the stabilities of each parameter regions using computer
simulations XPPAut and MatCont. Since a HH model consists of 4-differential
equations, scientists have reduced the HH model to two-parameters differential
equations to reduce the computational load of a more complex neuronal study.
Reduced models such as the FitzHugh-Nagumo (FHN) and Morris-Lecar (ML)
models are supposed to be able to explain the dynamical view of the mechanism of a
single neuron in a better or simpler way without losing any dynamical properties
from the original modelling.
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