A Class of Models for Mutual Entrainment of an Ensemble of Neurons

Abstract

In the preceding chapter, the question has been raised: How can the Orcadian wake-sleep rhythm be so precise in its timing? A possible answer to this question, to be considered here, is that one might be able to construct a very reliable pacemaker out of an array of cellular components which are individually far less reliable: units which are very erratic in their cycle-to-cycle behavior, and which, while similar to each other in basic functioning, differ appreciably one from another in their quantitative characteristics. If a precise pacemaker is to emerge from the behavior of a heterogeneous ensemble of “sloppy” cellular elements, those components must interact with each other in some sort of a nonadditive fashion, and this chapter is ultimately concerned with a formulation of how coupling of that sort might take place. As a necessary prelude to that formulation, however, we must consider in some detail the behavior of the erratic elements of which the ensemble is composed, when they are acting in complete independence of each other.