QUALITATIVE-ANALYSIS OF MYELINATED NERVE-FIBERS WITH POINT-NODE FITZHUGH-NAGUMO DYNAMIC SYSTEM

The equations for the membrane potentials in a point-node myelinated axon fibers model take the form U(t) = U(xx) - GU, x is-an-element-of (0,1) mod (1), W = 0, x is-an-element-of (0, 1) mod (1), U(t) = M[U(x)]x + F(U) - W, x = 0 mod (1), W(t) = sigma-U - gamma-W, x = 0 mod (1), [U]x = 0, x = 0 mod (1), where U = (u1, u2, ..., u(n))t, W = (w-1, w-2, ..., w(n))t, M = LAMBDA-I - alpha-B and the model dynamics are of FitzHugh-Nagumo type. In this paper, two new results for this model are presented. In the first result it is shown that this model has two nontrivial solutions and the contracting rectangle technique is used to show that one of these solutions is stable. The second result gives an existence proof for the Cauchy problem associated with this model.