Modeling of Nerve System by Differential Equations Theory, M.Sc. Thesis Sharif University of Technology ; Fotuhi, Morteza (Supervisor)
Abstract
In this thesis, behavior of a single neuron and a collection of neurons, has modeled by using ordinary differential equation techniques. In modeling of a single neuron, cell’s potential and parameters related to ion’s are variables of differential equation. Often some of this variables change very faster than the others. That causes using small perturbation methods in modeling. The Hodgkin-hoxley equations identified as main model and its reduced models used in thesis. In modeling of a network of neurons, there are also synaptic and neuron variables and also they change in different speeds, too. That again leads us to small perturbation theory. Synapses are hyperpolarizing and depolarizing....
Cataloging briefModeling of Nerve System by Differential Equations Theory, M.Sc. Thesis Sharif University of Technology ; Fotuhi, Morteza (Supervisor)
Abstract
In this thesis, behavior of a single neuron and a collection of neurons, has modeled by using ordinary differential equation techniques. In modeling of a single neuron, cell’s potential and parameters related to ion’s are variables of differential equation. Often some of this variables change very faster than the others. That causes using small perturbation methods in modeling. The Hodgkin-hoxley equations identified as main model and its reduced models used in thesis. In modeling of a network of neurons, there are also synaptic and neuron variables and also they change in different speeds, too. That again leads us to small perturbation theory. Synapses are hyperpolarizing and depolarizing....
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