Quasi-discreted dynamics of a neural net: The lighthouse model - Hermann Haken (Discrete Dynamics in Nature and Society)
This paper studies the features of a net of pulse-coupled model neurons, taking into account the dynamics of dendrites and axons. The axonal pulses are modelled by δ-functions. In the case of small damping of dendritic currents, the model can be treated exactly and explicitly. Because of the δ-functions, the phase-equations can be converted into algebraic equations at discrete times. We first exemplify our procedure by two neurons, and then present the results for N neurons. We admit a general dependence of input and coupling strengths on the neuronal indices. In detail, the results are