This article is part of a special issue on Neuronal Dynamics of Sensory Coding.

Abstract The joint influence of recurrent feedback and noise on gain control in a network of globally coupled spik-ing leaky integrate-and-fire neurons is studied theoretically and numerically. The context of our work is the origin of divisive versus subtractive gain control, as mixtures of these effects are seen in a variety of experimental systems. We focus on changes in the slope of the mean firing frequency-versus-input bias ( f –I) curve when the gain control signal to the cells comes from the cells ’ output spikes. Feedback spikes are modeled as alpha functions that produce an addi-tive current in the current balance equation. For generality, they occur after a fixed minimum delay. We show that purely divisive gain control, i.e. changes in the slope of the f –I curve, arises naturally with this additive negative or positive feedback, due to a linearizing actions of feedback. Nega-tive feedback alone lowers the gain, accounting in particular for gain changes in weakly electric fish upon pharmacolog-ical opening of the feedback loop as reported by Bastian (J Neurosci 6:553–562, 1986). When negative feedback is sufficiently strong it further causes oscillatory firing patterns which produce irregularities in the f –I curve. Small positive feedback alone increases the gain, but larger amounts caus