Distributed delays stabilize neural feedback systems

We consider the effect of distributed delays in neural feedback systems. The avian optic tectum is reciprocally connected with the isthmic nuclei. Extracellular stimulation combined with intracellular recordings reveal a range of signal delays from 3 to 9 ms between isthmotectal elements. This observation together with prior mathematical analysis concerning the influence of a delay distribution on system dynamics raises the question whether a broad delay distribution can impact the dynamics of neural feedback loops. For a system of reciprocally connected model neurons, we found that distributed delays enhance system stability in the following sense. With increased distribution of delays, the system converges faster to a fixed point and converges slower toward a limit cycle. Further, the introduction of distributed delays leads to an increased range of the average delay value for which the system's equilibrium point is stable. The system dynamics are determined almost exclusively by the mean and the variance of the delay distribution and show only little dependence on the particular shape of the distribution.