Periodically forced leaky integrate-and-fire model - art. no. 041907

The discharge pattern of periodically forced leaky integrate-and-fire model s is studied. While previous analyses have been mainly concerned with the r esponse of this model to sinusoidal stimulation, our results hold for arbit rary periodic inputs. It is shown that, for any periodic input, the map rep resenting the relation between input phases at consecutive discharge times can be restricted to a piecewise continuous, orientation preserving circle map. This implies that (i) the rotation number is well defined and independ ent of the initial condition, and (ii) in the same way as for sinusoidal fo rcing, other forms of periodic stimuli can evoke only one of four types of response, namely, phase locking, quasiperiodic discharges, nonchaotic aperi odic firing, and termination of the discharge after a finite number of firi ngs.