Measuring Chaos in the Brain: A Tutorial Review of Nonlinear Dynamical Eeg Analysis

Nonlinear dynamical systems that are open, dissipative, and subject to strong non-equilibrium constraints are capable of self-organization, the spontaneous emergence of large scaJe, complex behavior (Nicolis & Prigogine, 1989). One variety of self-organization that can be produced by such systems is deterministic chaos (popularly, “chaos”). Although chaos was first described by Poincar6 in the 1800s, recent years have witnessed major developments in the physics of chaotic systems (Crutchfield, Farmer, Packard, & Shaw, 1986; Eubank & Farmer, 1990; Glass & Mackey, 1988; Gleick, 1987; Guevara, Glass, Mackey, & Shrier, 1983; Middleton, 1990; Schuster, 1988; Stewart, 1989; Tsonis & Tsonis, 1989; van Rossum & de Bie, 1991). Beginning in the mid 1980s, scientists began to apply chaos theory to the human electroencephalogram, or EEG (Albano et al., 1986; Babloyantz & Destexhe, 1986; Bab-loyantz, Salazar, & Nicolis, 1985; Dvořák & ŠIška, 1986; Dvořák, ŠIška, Wackermann, Hrudová, & Dostálek, 1986; Holzfuss & Mayer-Kress, 1986; Layne, Mayer-Kress, & Holzfuss, 1986; Rapp et al., 1985; for pioneering thoughts, see Basar, 1983a, 1983b; this literature will be reviewed in greater detail below).