The Netlet Theory and Cooperative Phenomena in Neural Networks

Abstract

Many of the observed oscillatory phenomena in biological systems are the result of endogenous neural activity and occur in the absence of any kind of proprioceptive feedback. In certain simple animals such activity is manifested in a stereotyped behavioral response of considerably longer duration than the evoking stimulus. For instance, in Tritonia gilberti (a slug-like nudibranch) even the briefest touch by a predator triggers a powerful escape motion consisting of alternating dorsal and ventral flections of the animal’s body. Physiological studies by A. O. D. Willows revealed that the mechanism responsible for this behaviour is a cooperative effect which requires the interaction between three small pools of neurons. In our earlier publications we have proposed a netlet theory for investigating the dynamics of interacting neuronal ensembles. We found that a variety of cooperative phenomena, such as hysteresis effects, phase transitions, resonances and entrainments exist in such structures. By a combination of mathematical analysis and computer simulation it is shown in this paper that hysteresis effects together with a known property of neurons, namely, accumulating hyperpolarization, give rise to the kind of behavior observed in Tritonia and shed light on some features found in the single unit firing records.