Neurodynamics

Introduction to the nonlinear dynamics of neurons and simple neural systems through nonlinear dynamics, bifurcation theory, and chaotic motions. The dynamics of single cells is considered at different levels of abstraction, e.g., biophysical and "reduced" models for analysis of regularly spiking and bursting cells, their dynamical properties, and their representation in phase space. The dynamics of synaptic plasticity is studied based on relative timing of neural spikes. Advanced topics such as spatiotemporal dynamics of EEG will be presented in guest lectures. Homework exercises and an in-class computational laboratory will accompany the lectures, and students will work in groups on a final project. Requirements include in-class presentation and submission of a final project report.

Projects will be drawn from a range of topics in computational modeling and analysis of dynamics in biological and engineered neural systems, based on the research interests of the students. Interdisciplinary approaches are highly recommended, such as projects involving VLSI design of dynamical neural systems implemented in silicon circuits.