Phase-Locking in a General Class of Integrate and Fire Models

This paper studies phase-locking in a network of N neurons. The dynamic variables are the phases of the axonal pulses as well as the dendritic currents. The coupling via synaptic strengths may be arbitrary, up to a specific constraint. Arbitrary time delays of pulses and dendritic currents are included. The class of integrate and fire models treated here is characterized by a great variety of dendritic response functions (Green's functions). We determine the phase-locked state, the pulse interval, and present the stability equation for the case in which the dendritic response function is Rall's α-function, but still arbitrary couplings and delays are admitted.