Phase locking in the lighthouse model of a neural net with several delay times

Abstract

This paper studies the features of a net of N pulse-coupled model neurons, taking into account the dynamics of dendrites and axons. The axonal pulses are modeled by δ-functions. We admit a general dependence of the coupling strengths on the neuronal indices. In detail, the results are 1. exact solution of the phase-locked state for delayed interactions with several delay times 2. stability analysis of phase-locked state. Delays cause relaxation oscillations of the pulse rate. In general, increasing delay times increase relaxation times 3. beyond critical coupling strength exponential increase of pulse rate of phase-locked state 4. under different conditions instabilities occur leading to spatio-temporal patterns of neural firing rates.