Pulse replication and slow absolute spectrum in the FitzHugh--Nagumo system
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.
Password: “arizona” (all lower case)