ASYMPTOTIC-BEHAVIOR AND STEADY-STATE SOLUTIONS OF A MYELINATED AXON MODEL WITH FITZHUGH NAGUMO DYNAMICS

A mathematical model of a myelinated nerve fiber is used in which the fiber has passive loading between nodes and has FitzHugh-Nagumo dynamics on each node. Existence of steady state solutions is investigated by superimposing phase diagrams of the nodal and internodal (myelin) equations. The stability of steady state solutions is investigated by construction of an appropriate Liapunov function; the trivial solution is an attractor. It is found that if the length of the nodal segments is sufficiently large compared to the length of the internodal segments, there are always nontrivial, stable 1-periodic steady state solutions. For the shorter nodal segments, stability and even existence of nontrivial 1-periodic steady state solution may fail. © 1990.