Mathematical Frameworks for the Study of Oscillatory Networks in Neuroscience

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Kazemi, Seakineh | 2020

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 53953 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Fotouhi Firouzabad, Morteza
Abstract:
In this thesis, we first introduce the required biological preparations and popular models for modeling single neuron, synapse and cable. Then by introduction of limit cycle oscillators and the necessary prerequisites, investigations are limited to systems involving weakly coupled oscillators. As two examples of such models, famous Kuramoto and Wilson- Cowan models are described. In the following, we introduce some methods for reduction dimension of weakly coupled oscillators and finally we apply one of the expressed methods on the dynamics of cortical network
Keywords:
Limit Cycle Oscillation ; Koopman Operator ; Phase Reduction Method ; Weakly Coupled Oscillators ; Oscillator Network ; Neuroscience

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