A dynamical system study of the Hodgkin-Huxley Model of nerve membrane
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Equations of the Hodgkin and Huxley model of action potentials in squid giant axons have been studied and described in this thesis. Explanation of the development of the space clamp model that won its authors the Nobel Prize for Physiology and Medicine in 1963 is provided since it is still one of the key mathematical models in the study of neural communications today. A numerical approach was used to obtain solutions to their model. The computer code used will be provided. More modern approaches to analyzing these models will be explored and discussed as a study of dynamical systems. A reduced Hodgkin-Huxley model will be explained and analyzed using modern methods. A set of problems will be included for those who wish to be guided through parts of the development of the models.