SINGLE EFFECTIVE NEURON

We consider a network of N symmetrically interconnected neurons. Through the procedure of adiabatic elimination (separation of time scales), the dynamics of a single neuron is obtained, in closed form, from the system of coupled differential equations that describe the N-neuron problem. For the deterministic case, our approach yields an explicit form for the single-neuron "self-coupling" term J11. The case of noisy neurons containing both Langevin and multiplicative noise (in the synaptic connections) is also considered.