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

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 delta-functions. We admit a general dependence of the coupli ng strengths on the neuronal indices. In detail, the results are 1. exact solution of the phase-locked state for delayed interactions with s everal delay times 2. stability analysis of phase-locked state. Delays cause relaxation oscill ations of the pulse rate. In general, increasing delay times increase relax ation times 3. beyond critical coupling strength exponential increase of pulse rate of phase-locked state 4. under different conditions inst abilities occur leading to spatio-tempor al patterns of neural firing rates.