Excerpt: For half a century, threshold has been known to be important in the activities of nerve cell and synapse, but little is known of the general properties that so ubiquitous a feature must impose on the system’s behaviour in the large. Beurle1, in his investigations of the transmission of waves of activity over a conducting not, noticed that a net with threshold would have a marked tendency to be unstable, but his assumptions were complex, and the origin of the instability is not easily identified. Here we propose to show that an instability, similar to his, can readily be traced from a simpler origin.

For half a century, the widespread occurrence of threshold in the nervous system, and the importance of threshold in the details of neuronic activity, have been well known. There is less known, however, about how threshold would show in the large – in the behavior of the organism as a whole. Two studies (Beurle, 1956; Farley and Clark, 1961) have been made of the behavior of waves of activity traveling through a nerve net. Both studies have shown that such a net would have difficulty in maintaining a steady activity, for the wave of activity tends either to die out completely or to increase to saturation. Far from being tractable and steady, from the standpoint of biological usefulness such a network displays an essential instability. Not only does it tend rapidly to the extremes of inactivity or activity, but, once there, it can be moved away from the extreme only with difficulty. This finding deserves emphasis because it is quite contrary to the plausible idea that threshold stabilizes a network. It also suggests that the actual brain must incorporate some mechanism that actively opposes the instability. The studies cited are complex and do not allow the instability and the threshold to be related directly and simply. Here, we shall show that an extremely general and simple rr.odel still allows the relation to be displayed clearly. It also allows us to see more readily what is essential.