Synthetic analysis of periodically stimulated excitable and oscillatory membrane models

Many excitable neuronal membranes become oscillatory when stimulated by lar ge enough de currents. In this paper we investigate how the transition from excitable to oscillatory regimes affects the response of the membrane to p eriodic pulse trains. To this end, we examine how the dynamics of periodica lly stimulated FitzHugh-Nagumo neuron model changes as the system switches from excitability to oscillation. We show that, despite the important chang e in the asymptotic dynamics of the unperturbed model, p:q phase-locking (i .e., the model membrane discharges q times in p interstimulus intervals and q input-output intervals repeat periodically) regions in the stimulus peri od-stimulus amplitude parameter plane (Arnold tongues) change continuously when the model changes from excitable to oscillatory. We provide further ev idence for the continuous change of the Arnold tongues by using an analytic ally tractable one-dimensional map that approximates the Poincare map of th e forced system. We argue that the smooth change in the Arnold tongues resu lts from the fact that, despite the qualitative difference between the asym ptotic dynamics of unforced excitable and oscillatory regimes, other aspect s of the dynamics such as the wave form of individual action potentials, ar e similar in the two regimes. [S1063-651X(99)04701-7].