• Daniel Dewoskin
  • October 19, 1 PM
  • 2866 East Hall

In 1963, Hodgkin and Huxley won the Nobel prize in medicine for their work modeling action potentials in the squid giant axon. In this talk, I will give an introduction to the full Hodgkin-Huxley equations, which model the neuron as an electrical circuit, and then discuss the reduced Morris-Lecar model, for which analysis is more tractable. I will describe the distinct types of behavior that the model exhibits based on bifurcations in the phase space, as well as geometric singular perturbation theory. Finally I will show some applications of the Morris-Lecar model to studying coupled systems of neurons, and discuss the introduction of noise into the system. This talk will be accessible to graduate students and undergraduate students who are familiar with dynamical systems.