Special topics course offered in Fall 2022 by Hannah Choi.
Familiarity with dynamical systems and either MATLAB or Python.
There will be no textbook requirement, but topics and materials will be adapted from 1) “Neuronal Dynamics” by Gerstner, Kistler, Naud, and Paninski; 2) “Dynamical Systems in Neuroscience” by Izhikevich; and 3) Some key classical papers in the field. Grades will be based on problem sets and a term project.
This course will cover mathematical analysis and simulation of neural systems across single cells, networks, and populations, employing methods from dynamical systems, network science, and stochastic processes. The topics will include single-neuron excitability and bifurcation, network structure and synchrony, and statistical dynamics of large neural populations. More specifically, here is the list of potential topics that will be covered in the course:
1. Nonlinear dynamics of single neurons
a. Bifurcations in single neurons
b. Timescale separation in generalized integrate and fire models
c. Data-driven, reduced neuronal models
2. Spiking dynamics
a. Spike time correlations
b. Lyapunov exponents, attractors
c. Information measures in spike trains
3. Population dynamics
a. Diffusion approximations and stochastic-differential equations
b. Mean-field models
c. Balanced networks
4. Learning and neural networks
a. Spike-time-dependent plasticity
b. Recurrent neural networks
5. (If time permits) Understanding brain networks
a. Local & global network measures
b. Generative models of brain networks