Dynamics of Neural Fields Models With Delay

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Sepahvand, Amin | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 43260 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Fotuhi Firoozabad, Morteza
Abstract:
Neural field models with delays define a useful framework for modeling macroscopic parts of the cortex involving several populations of neurons. Nonlinear delayed integrodi fferential equations describe the spatio-temporal behavior of these fields. We also present a study of the numerical computation of these solutions in a special case. Another original contribution of ours is the definition of a Lyapunov functional and the result of stability it implies. We illustrate our work on a variety of examples that are relevant to modeling in neuroscience.
Keywords:
Neural Fields ; Stability ; Delay Equations