MATH 723: Mathematical Neuroscience

Instructor: Georgi Medvedev

Office hours: R 5-5:50

Office: 292 Korman Center

E-mail: medvedev@drexel.edu
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The course web page from the last year is here.

Syllabus

Lecture notes:

Lecture 1: The Hodgkin-Huxley model. ps   pdf
Lecture 2: Approximate systems.   ps
Lecture 3: Elements of the theory of differential equations.   ps
Lecture 4: Elements of the bifurcation theory.   ps
Lecture 5: The homoclinic bifurcation.   ps
Lecture 6: Bursting (slides).   ps

Codes:

hh.ode (The Hodgkin-Huxley model)
chay.ode (The Chay model)   fast.ode (fast subsytem)
hh.ode (NaP+K+KM model of bursting neuron)

Reading:

M. Rabinovich, P. Varona, A.I. Selverston, H.D.I. Abarbanel, Dynamical principles in neuroscience, pdf
J. Gao and P. Holmes, On the dynamics of electrically-coupled neurons with inhibitory synapses, pdf
F. K. Skinner, N. Kopell, E. Marder, Mechanisms for Oscillation and Frequency Control in Reciprocally Inhibitory Model Neural Networks, pdf

Student Presentations:
Bifurcation, bursting and spike frequency adaptation.
Leach heart Half-center oscillator.
Seizure suppression in a human cortical model.
The Wilson-Cowan model.
Interspike interval variability.