Topic: Synthesizing Chaos without Nonlinear Dynamics
Speaker: Dr. Ned J. Corron, U.S. Army RDECOM
Date & Time: Thursday, Nov. 16, 2006, 1:00 PM
Place: Room 140 VMC (Chambers Hall)
Chaos is usually attributed only to nonlinear dynamical systems. Yet surprisingly, it was recently shown that chaotic waveforms can also be synthesized by linear superposition of equally spaced but randomly polarized basis functions. The basis function contains an infinitely long, exponentially increasing oscillation that terminates in a large pulse. We observe that this function is easily realized when viewed backward in time as a pulse followed by ringing decay. Consequently, a linear, second-order filter driven by randomly polarized square pulses generates an output waveform that, when viewed backward in time, exhibits the essential qualities of chaos, including determinism and a positive Lyapunov exponent. Surprisingly, using different encodings of the random binary source, the same filter can produce multiple topologically distinct chaotic sets, including both Lorenz-like butterfly and Rossler-like folded band waveforms. We demonstrate that synthesizing chaos requires a careful balance between the topological entropy of the random source and dissipation in the linear filter. We also show that the different drive encodings can be viewed as grammar restrictions on a more general encoding that produces a chaotic superset encompassing both the Lorenz butterfly and Rossler folded band paradigms of nonlinear dynamics. Thus, the language of deterministic chaos provides a useful description for a wide class of signals not generated by a nonlinear dynamical system. This phenomenon suggests that chaos may be connected to physical theories whose underlying framework is not that of a traditional deterministic nonlinear dynamical system.
Dr. Corron obtained his Ph.D. in Applied Mathematics from Northwestern University in 1989. He worked as an analyst for Dynetics Inc., in Huntsville, Alabama, from 1990 to 2000. Currently he works for the US Army Aviation and Missile Research, Development and Engineering Center (AMRDEC) at Redstone Arsenal, where he is part of a research group in quantum optics and nonlinear dynamics.
Refreshments will be served at 12:45 PM