Linear response theory (LRT) can be used to compute spectral properties of single and populations of stochastic leaky integrate-and-fire neurons. The effects of inputs, both external and from delayed feedback, can be modeled within that theory when the neural function is sufficiently linearized by noise. It has been used to explain experiments where gamma oscillations are induced by spatially correlated stochastic inputs to a network with delayed inhibitory feedback. Here we expand this theory to include two distinct population types. We first show how to deal with homogeneous networks where both types of neurons have identical intrinsic properties. We further tackle the asymmetric case, where noise or bias differ. We also analyze the case where the membrane time constants differ, based on experimental evidence, which requires delicate alterations of the theory. We directly apply the theory to networks of ON and OFF cells in the electrosensory system, which together provide global delayed negative feedback to all cells; however, ON and OFF cells receive external inputs of opposite polarities. Theoretical results are in excellent agreement with numerical simulations of the two population network. In contrast to the case of a single ON cell population with feedback, the more realistic presence of both cell types can significantly reduce the propensity of the delayed feedback network to oscillate for spatially correlated inputs. Our results are further linked to recent predictions from deterministic neural field theory. Among other findings, our work suggests that the observed gamma oscillations could be explained only if the ON and OFF cell feedback pathways are anatomically segregated. Thus our two population LRT can make specific predictions about network topography in specific systems.

• Received 7 December 2012

DOI:https://doi.org/10.1103/PhysRevE.87.032703