Lasers and Brains: Complex Systems with Low-Dimensional Attractors

The quantification of complex dynamical phenomena associated with motions on strange attractors has made available a tool of considerable power for the analysis of systems which display aperiodic or apparently random temporal behavior. Until recently, aperiodic phenomena were described primarily in terms of snapshots of time sequences, power spectra, or correlation functions. These made possible some qualitative or pictorial analyses but did not provide simple numerical criteria suitable for more quantitative studies. During the past decade, spectral studies have made possible the identification of a few characteristic routes to apparently chaotic behavior in hydrodynamic[l–3], chemical [4], optical [5–7, 16, 29], and electronic [8, 9] systems. There were very strong indications that the complex motions, characterized by broadband spectra, to which these routes led, were in fact motions on strange attractors.