Periodically forced leaky integrate-and-fire model

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Abstract
The discharge pattern of periodically forced leaky integrate-and-fire models is studied. While previous analyses have been mainly concerned with the response of this model to sinusoidal stimulation, our results hold for arbitrary periodic inputs. It is shown that, for any periodic input, the map representing 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 independent of the initial condition, and (ii) in the same way as for sinusoidal forcing, other forms of periodic stimuli can evoke only one of four types of response, namely, phase locking, quasiperiodic discharges, nonchaotic aperiodic firing, and termination of the discharge after a finite number of firings.