Strange Attractors, Chaotic Behavior, and Information Flow

Abstract

Simple system equations displaying turbulent behavior are reviewed in the light of information theory. It is argued that a physical implementation of such equations is capable of acting as an information source, bringing into the macroscopic variables information not implicit in initial conditions. The average rate of information production ƛ is a system state function, and is given for simple cases by a “Liapunov characteristic exponent”, developed by Oseledec. The transition of a system from laminar to turbulent behavior is understandable in terms of the change of X from negative to positive, corresponding to the change of the system from an information sink to a source. The new information of turbulent systems precludes predictability past a certain time; when new information accumulates to displace the initial data, the system is undetermined. The observed geometry of stränge attractors is seen to arise naturally from a rule allowing joining but not Splitting of trajectories in phase space. The phenomenology of stränge attractors in three dimensions is discussed, and a basis for their classification suggested. A comment is made on the commonplace occurrence of information producing systems in the real world, and on their possible relation to 1/f noise. © 1981, Walter de Gruyter. All rights reserved.