Entrainment, Arnold tongues, and duality in a periodically driven integrate-and-fire model
We have studied an integrate-and-fire model neuron driven by a periodic sequence of Gaussian-shaped 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 firing 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 find 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.
entrainment arnold tongues integrate-and-fire model duality transformation