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Effects of Dynamics and Structure on Population-level Oscillations in Homogeneous Neuronal Networks

Vatandoost kamali, Maryam | 2015

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 47193 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Razvan, Mohammad Reza; Sharifi Tabar, Mohsen
  7. Abstract:
  8. Networks of neurons produce diverse patterns of oscillations, arising from the net-work’s global properties, the propensity of individual neurons to oscillate, or a mixture of the two. Here we describe noisy limit cycles and quasi-cycles, two related mech-anisms underlying emergent oscillations in neuronal networks whose individual com- ponents, stochastic spiking neurons, do not themselves oscillate. Both mechanisms are shown to produce gamma band oscillations atthepopulation level while individualneu-rons fire at a rate much lower than the population frequency. Spike trains in a network undergoing noisy limit cycles display a preferred period which is not found in the case ofquasi-cycles,due to theeven faster decay of phase information inquasi-cycles. These oscillations persist in sparsely connected networks, and variation of the network’s con-nectivity results in variation of the oscillation frequency. A network of such neurons behaves as a stochastic perturbation of the deterministic Wilson-Cowan equations, and
    the network undergoes noisy limit cycles or quasi-cycles depending on whether these have limit cycles or a weakly stable focus. These mechanisms provide a new perspec-tive on theem emrgence of rhythmic firing in neural networks, showing the coexistence of population-level oscillations with very irregular individual spike trains in a simple and general framework
  9. Keywords:
  10. Power Spectral Analysis ; Homogeneous Neural Network ; Emergent Oscillations ; Firing Rate ; Wilson-Cowan Equation

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