EXOTIC DYNAMIC BEHAVIOR OF THE FORCED FITZHUGH-NAGUMO EQUATIONS

Space-clamped FitzHugh-Nagumo nerve model subjected to a stimulating e lectrical current of form I-o + I cos gamma t is investigated via Poin care map and numerical continuation. If I = 0, it is known that Hopf b ifurcation occurs when I-o is neither too small nor too large. Given s uch an I-o. If gamma is chosen close to the natural frequency of the H opf bifurcated oscillation, a series of exotic phenomena varying with I are observed numerically. Let 2 pi lambda/gamma denote the generic p eriod we watched. Then the scenario consists of two categories of peri od-adding bifurcation. The first category consists of a sequence of hy steretic, lambda --> lambda + 2 period-adding starting with lambda = 1 at I = 0+, and ending at some finite I, say I, as lambda --> infinit y. The second category contains multiple levels of period-adding bifur cation. The top level consists of a sequence of lambda --> lambda + 1, period-adding starting with lambda = 2 at I = I. From this sequence, a hierarchy of m --> m + n --> n, period-adding in between are derive d. Such a regular pattern is sometimes interrupted by a series of chao s. This category of bifurcation also terminates at some finite I. Harm onic resonance sets in afterwards. Lyapunov exponents, power spectra, and fractal dimensions are used to assist these observations.