ASA 124th Meeting New Orleans 1992 October

4aMU1. An introduction to chaos and its control.

Manfred R. Schroeder

Univ. of Gottingen, Gottingen, Germany

AT&T Bell Labs., Murray Hill, NJ 07974

Nonlinear dynamic systems often show sensitive dependence on initial conditions leading to unpredicable behavior with eponentially growing uncertainty. Despite the perfect determinism of the underlying physical laws, such systems are characterized by chaotic behavior, called deterministic chaos. Chaos is encountered in many nonlinear systems from the double pendulum to the three-body problem. The malfunction of the vocal chords and turbulence in wind instruments are examples of acoustic chaos. This paper is intended as an introduction to chaos, its control, and the related concepts of fractals and self-similarity [M. Schroeder, Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise (Freeman, New York, 1991)].