State Predictability and Information Flow in Simple Chaotic Systems

Abstract

The possibility of state prediction in deterministic chaotic systems, which are described by 1-D maps, is discussed in the light o f information theory. A quantity h(l) is defined which represents the production of uncertainty on a future state by the chaotic dynamics (intrinsic noise) after / time steps have passed. h(l) is related to the Lyapunov characteristic exponent. Moreover, the influence of the measuring process (overlappings o f mapped boxes o f state space partition) and external noise on the state predictability are investigated quantitatively.