Steady-state and limit cycle activity of mass of neurons forming simple feedback loops (I): lumped circuit model

Abstract

The neurons in the mammalian olfactory bulb sustain two types of synaptic feedback. The periglomerular cells excite each other and form a positive feedback loop. The mitral-tufted cells are excited by periglomerular neurons, and they excite granule cells and are inhibited by them. The last two neural populations form a negative feedback loop. This work contains mathematical proofs for the existence of steady state unvarying activity in periglomerular neurons, and of steady state oscillatory activity of mitral-tufted and granule cells, which is manifested in the EEG. The following predictions are made. 1) The level of mean ongoing pulse activity of the periglomerular population is determined by peripheral sensory and centrifugal input. 2) The interaction of mitral and granule populations determines a limit cycle detectable in the EEG. 3) The frequency of the limit cycle is determined by periglomerular and centrifugal input. 4) The steady and oscillatory pulse rates are stable, and if they are perturbed, they return to the levels preceding perturbation.