Stochastic mode-locking for a noisy integrate-and-fire oscillator

We investigated the ways in which noise influences lower-order mode-locked regions (Arnold tongues) in the parameter space of an integrate-and-fire mo del with a periodically modulated threshold. To study the stochastic mode-l ocking in the model, we use the first-passage-time problem of the Ornstein- Uhlenbeck process with a periodic boundary to define the Markov operator go verning the transition of a threshold phase density. We present a numerical method for evaluating stochastic bifurcation by spectral analysis of the o perator and briefly discuss the implications for biological systems. (C) 20 00 Elsevier Science B.V. All rights reserved.