Stabilized Dynamics in Physiological and Neural Systems Despite Strongly Delayed Feedback

Abstract

Interaction delays are ubiquitous in feedback systems due to finite signal conduction times. An example is the hippocampal feedback loop comprising excitatory pyramidal cells and inhibitory basket cells, where delays are introduced through synaptic, dendritic and axonal signal propagation. It is well known that in delayed recurrent systems complex periodic orbits and even chaos may occur. Here we study the case of distributed delays arising from diversity in transmission speed. Through stability considerations and numerical computations we show that feedback with distributed delays yields simpler behavior as compared to the singular delay case: oscillations may have a lower period or even be replaced by steady state behavior. The introduction of diversity in delay times may thus be a strategy to avoid complex and irregular behavior in systems where delayed regulation is unavoidable.