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Determinism in synthesized chaotic waveforms.

Ned J Corron1, Jonathan N Blakely, Scott T Hayes

  • 1US Army RDECOM, AMSRD-AMR-WS-ST, Redstone Arsenal, AL 35898, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 4, 2008
PubMed
Summary
This summary is machine-generated.

Synthesized waveforms viewed backward in time exhibit determinism. This rigorously demonstrates that reverse-time signals from linear filters can mimic deterministic chaotic systems, revealing hidden order in seemingly random processes.

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Area of Science:

  • * Signal processing and nonlinear dynamics.
  • * Theoretical physics and complex systems analysis.

Background:

  • * Linear filters typically produce predictable outputs when time-ordered forward.
  • * Randomly polarized square waves introduce stochasticity into filter inputs.
  • * Reversing time in dynamical systems can reveal underlying deterministic properties.

Purpose of the Study:

  • * To investigate the temporal behavior of linear filter outputs when time-reversed.
  • * To determine if reverse-time synthesized waveforms exhibit deterministic characteristics.
  • * To establish a rigorous link between linear filter outputs and deterministic chaotic systems.

Main Methods:

  • * Analysis of a linear filter driven by a randomly polarized square wave.
  • * Embedding the system's output into a three-dimensional state space.
  • * Examination of the time-reversed output for deterministic properties.
  • * Comparison with established criteria for deterministic chaos, including Lyapunov exponents.

Main Results:

  • * The time-reversed output of the linear filter demonstrates deterministic behavior at all points in time.
  • * The system, when analyzed in a three-dimensional state space, shows consistent determinism.
  • * Exponential divergence, indicative of a positive Lyapunov exponent, was confirmed for the reverse-time waveforms.

Conclusions:

  • * Reverse-time synthesized waveforms from linear filters are deterministic.
  • * These waveforms convincingly emulate the behavior of deterministic chaotic systems.
  • * The study rigorously proves that seemingly random, time-reversed signals can originate from deterministic chaotic processes.