Modeling of Nerve System by Differential Equations Theory

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Keramati Tavallayi, Mohammad Mahdi | 2009

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 39922 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Fotuhi, Morteza
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. A very interesting question that we have discussed in thesis is if synaptic properties influence on synchronization in behavior?
Keywords:
Neuron ; Bifurcation ; Stochastic Perturbation ; Neurous System ; Differential Equation ; Hodgkin-Hoxley Equations

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