The nature of dominant Lyapunov exponent and attractor dimension curves of EEG in sleep

The dynamical behaviour of the brain is currently being viewed from the perspective of nonlinear dynamics. There are several reports of low dimensional chaotic activity in various states of human behaviour. The time evolution of chaotic systems exhibit many transitional states and brain is known to undergo a number of transitions in sleep. It evolves from random looking states to almost periodic states with an increase in the depth of sleep. There occurs intermittent random-like behaviour in REM (rapid eye movement) sleep. In this paper, we examine the transitional processes of brain activity in sleep from the patterns of attractor dimension (D-2) and its corresponding dominant Lyapunov exponent (lambda(1)) curves of EEG signals. Results indicate the occurrence of different degrees of chaoticity in the transitional states that may be related to various sleep stages. The chaotic parameter curves yield an objective measure of the neurodynamics of sleep comparable to an hypnogram. The parallelism of D-2 and lambda(1) curves implies the validity of Kaplan-Yorke conjecture for EEG. It is suggested that the nonlinear dynamical measures of EEG may yield information about the nature of underlying neural processes of brain in sleep.