The Existence and Stability of Classical Solutions in the Neural Fields Equations

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Shafiee, Ahmad | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 42778 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Fotouhi Firouzabadi, Morteza
Abstract:
In this thesis, first, the modeling method of neural fields is precisely presented. Then, Existence and Stability of different solutions of one dimensional neural fields like Standing Pulses, Traveling Waves and ... are investigated in three different models of neural fields. In order for proving Existence and Stability of the solutions the mathematical tools like Fourier transform and Evans function are applied. All the models which analysed in this thesis have the following Integro-Differential Equation form:
τ
∂u(x, t)
∂t
= −u(x, t) +
∫ +∞
−∞
w(x, y)f[u(y, t)]dy + I(x, t) + s(x, t)
and also in some models the parameters might be changed
Keywords:
Traveling Wave ; Neural Fields ; Integral Differential Equations ; Standing Pulses ; Evans Function

No TOC