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NJIT Mathematical Biology Seminar

Tuesday, September 25, 2007, 4:00pm
Cullimore Hall 611
New Jersey Institute of Technology

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The canard phenomenon and unexpected slow firing rates in a neural network with excitatory synaptic coupling

Martin Wechselberger

School of Mathematics and Statistics, University of Sidney, Australia

Recent work on Hodgkin-Huxley type neurons respectively neural networks showed a significant slowing of the firing rate of the network under certain circumstances. I show that 'canards' are responsible for that delay and that the corresponding relaxation oscillatory patterns observed are of mixed-mode type. I line out how to identify this canard phenomenon by using dynamical systems theory, in particular geometric singular perturbation theory.