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Pulse replication and slow absolute spectrum in the FitzHugh--Nagumo system

Analysis, Dynamics, and Applications Seminar

Pulse replication and slow absolute spectrum in the FitzHugh--Nagumo system
Series: Analysis, Dynamics, and Applications Seminar
Location: Online
Presenter: Paul Carter, School of Mathematics, University of Minnesota

The FitzHugh--Nagumo PDE is a simplified model of nerve impulse propagation, which is known to admit stable traveling pulse solutions. I will present existence and stability results for (multi)pulse solutions, and I will describe a phenomenon whereby a single pulse can be continuously deformed into a double pulse by parameter continuation. Along this transition, eigenvalues accumulate on the positive real axis due to the fact that the pulse solutions spend long times near a slow manifold which exhibits absolute spectrum.

 

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