Entrainment, Arnold tongues, and duality in a periodically driven integrate-and-fire model

We have studied an integrate-and-#re model neuron driven by a periodic sequence of Gaussianshaped current pulses of width 1=2N and amplitude . For large N the current is a sequence of delta pulses and for smaller N it approaches a sine. When N is large, the #ring rate f vs. curve is a staircase of entrainment steps yielding an Arnold tongue structure in the vs. plane. In the small N limit we #nd novel entrainment steps in the f vs. plane, without Arnold tongue structure. The steps in the two N regimes are related by a duality transformation. In the presence of noise in the pulse arrival times, the steps disappear above a critical noise value. c © 2002 Published by Elsevier Science B.V.