Associative Memory of a Pulse-Coupled Noisy Neural Network with Delays: The Lighthouse Model

We start from the basic equations of a pulse-coupled neural network with arbitrary couplings (“synaptic strengths”) between its elements. The axonal pulses are described by means of a phase, whose rotation speed depends on the dendritic inputs (“lighthouse model”). We include the effects of noise by means of fluctuating forces. We also allow for delays between the neurons. The introduction of time-averaged axonal pulse rates ω_ℓ allows us to convert the original, highly nonlinear and stochastic equations into rather simple equations for ui that can be solved directly. The solutions can be interpreted as action of an associate memory.