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UID:20260703T004756EDT-7929IJ8rrC@132.216.98.100
DTSTAMP:20260703T044756Z
DESCRIPTION:Title:An invariant winding number for the FiztHugh-Nagumo syste
 m\n\nAbstract:\n\nThe FitzHugh-Nagumo system of partial differential equat
 ions (FHN) is a generic model for excitable media\, often used to build a 
 qualitative understanding of electrophysiological phenomena. A well-charac
 terized traveling-pulse solution to FHN serves as a model for action poten
 tials in cardiac tissue and other contexts. The stability of the traveling
  pulse has been well-studied but the more global problem of predicting whe
 n an arbitrary initial condition will converge to the uniform rest solutio
 n and when it will converge to the traveling pulse remains unsolved. In th
 is talk\, I will present a proof of the existence of an invariant winding 
 number in an asymptotic limit of the FHN system (the singular FHN system -
  SFHN) on a circular 1D domain that provides a crucial step toward a globa
 l convergence result. I will also provide evidence that this SFHN winding 
 number result extends with limitations to FHN and outline conditions under
  which the SFHN approximation fails. The invariant winding number provides
  explanations for several observations of physiological relevance. For exa
 mple\, it explains the requirements on stimulus protocols that allow the f
 ormation and elimination of reentrant rhythms in cardiac tissue. This is j
 oint work with Kelly Paton.\n
DTSTART:20181015T200000Z
DTEND:20181015T210000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Eric Cytrynbaum (UBC)
URL:https://www.mcgill.ca/mathstat/channels/event/eric-cytrynbaum-ubc-29048
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