Analyzing Observed Chaotic Signals from Physical Systems

Henry Abarbanel, UC San Diego

Chaotic motion in nonlinear physical (and other) dynamical systems is found almost everywhere one looks. The tools for extracting characteristics of the system from the analysis of observed time series are now rather well established and quite useful for extracting new physical information about the source of the chaotic signals. The tools allow one to classify the signal unsing invariants such as Lyapunov exponents, separate chaotic and regular signals for noise reduction or communication using chaotic masking, make models of the evolution of the signal consistent with the instabilities causing the chaos, and even control the chaos to regular periodic orbits. We will describe the tools for this kind of signal analysis in the context of several interesting physical systems: 1) chaotic, low dimensional behavior in a high Reynolds number boundary layer flow 2) chaotic laser intensity fluctuations in a frequency doubled Nd:YAG laser 3) nonlinear circuits with chaotic evolution 4) proxy climate data from the observation of the Great Salt Lake.