Phase locking in integrate-and-fire models with refractory periods and modulation

It is known 8, 11, 16, 26] that phase locking can entrain frequency information when the leaky integrate-and-fire (IF) model of a neuron is forced by a periodic function. We show that this is still the case when the IF model is made more biologically realistic. We incorporate into our model spike dependent threshold modulation and refractory periods. Consecutive firing times from this model and their respective interspike intervals are related by an annulus map. We prove a general theorem concerning orientation reversing annulus twist homeomorphisms, which shows that our map admits a unique rotation number. This implies, in particular, that chaotic behaviour is not possible in our model and phase locking is predicted.This research was partially supported by NSF EIA-BITS grant 426411This research was partially supported by the Summer Undergraduate Research Program sponsored by IGERT grant NSF-DGE 9972824 and the Undergraduate Scholars Program at MSU-BozemanAcknowledgement The authors would like to thank Marcy Barge for discussions of prime ends and Sherry Heis for formatting the diagrams.