Exemplification of chaotic activity in non-linear neural networks obeying a deterministic dynamics in continuous time
K. E. Kürten, J. W. Clark · Cambridge University Press eBooks · 1988
Introduction During the last decade, a conspicuous theme of experimental and theoretical efforts toward understanding the behavior of complex systems has been the identification and analysis of chaotic phenomena in a wide range of physical contexts where the underlying dynamical laws are considered to be deterministic (Schuster, 1984). Such chaotic activity has been examined in great detail in hydrodynamics, chemical reactions, Josephson junctions, semiconductors, and lasers, to mention just a few examples. Chaotic solutions of deterministic evolution equations are characterized by (i) irregular motion of the state variables, and (ii) extreme sensitivity to initial conditions. The latter feature implies that the future time development of the system is effectively unpredictable. An essential prerequisite for deterministic chaos is non-linear response; and although there are famous examples of chaos in relatively simple systems (e.g. Lorenz, 1963; Feigenbaum, 1978), we expect this kind of behavior to arise most naturally in systems of high complexity. Since biological nerve nets are notoriously non-linear and are perhaps the most complex of all known physical systems, it would be most surprising if the phenomena associated with deterministic chaos were irrelevant to neurobiology. Indeed, there has been a growing interest in the detection and verification of deterministic chaos in biological preparations consisting of few or many neurons. At one extreme we may point to the pioneering work of Guevara et al . (1981) on irregular dynamics observed in periodically stimulated cardiac cells; and, at the other, to the recent analysis by Babloyantz et al . (1985) of EEG data from the brains of human subjects during the sleep cycle, aimed at establishing the existence of chaotic attractors for sleep stages two and four.