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Geometric Analysis of Synchronization in Neuronal Networks with Coupling Delays

Ramezanzadeh Barki, Sanaz | 2020

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53306 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Fotouhi Firouzabad, Morteza
  7. Abstract:
  8. We study synaptically coupled neuronal networks to identify the role of coupling delays in network synchronized behavior. Identifying the effect of delay is important for understanding information processing functions in the brain and Many studies have been done on the effects of delays on networks where the synapses are exclusively excitatory or inhibitory, but few address networks with both. Thus we focus on this case. In this thesis, we consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory and one inhibitory are coupled with time-delayed synapses. Using singular perturbation analysis, we will study the dynamic behavior of the network in terms of the existence of periodic solutions and their stability. Then we compare these results with delayless networks and perform numerical simulations to complete and validate the analytical results
  9. Keywords:
  10. Neural Networks ; Time Delay ; Synchronization Analysis ; Geometric Singular Perturbation ; Singular Perturbation ; Numerical Simulation

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