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NJIT Mathematical Biology Seminar
Tuesday, April 4, 2006, 4:00 pm
Cullimore Hall 611
New Jersey Institute of Technology
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How architecture restricts spiking patterns in phase oscillator networks
Courant Institute and the Center for Neural Science
New York University
We study networks of coupled phase oscillators and show that their architecture alone can force subsets to have the same frequencies for periodic solutions and the same winding numbers for general solutions. Our analysis follows the theory of coupled systems of ODEs in RN developed by Stewart, Golubitsky, Pivato, and Torok, which has a direct analog for networks of coupled phase oscillators. We then focus on applications in neural modelling, where ``spike" events driven by cells crossing specified phases are of primary interest. We show that, when individual cells in a neural network are described by phase or certain or integrate-and-fire dynamics, the network architecture plays a surprisingly strong role in restricting what spiking patterns can be produced and what features of these patterns are preserved over time. This is joint work with Kresimir Josic and Marty Golubitsky.
Last Modified: Jan 18, 2006
Victor Matveev
m a t v e e v @ n j i t . e d u