Chaos Without Nonlinear Dynamics

Abstract

Recently, it has been shown that chaos can be synthesized by the linear superposition of certain pulse basis functions. Here, we extend this result and show that a linear, second-order filter driven by a random signal can generate a waveform that is chaotic under time reversal. That is, the waveform exhibits determinism and a positive Lyapunov exponent when viewed backward in time. We demonstrate the filter using a passive electronic circuit, and the resulting waveform exhibits a Lorenz-like butterfly structure. This method for generating chaotic waveforms may be useful for a number of potential applications, including spread-spectrum communication and ultra-wideband (UWB) radar and ladar. The filter also demonstrates that chaos may be connected to physical theories beyond those described by a deterministic nonlinear dynamical system.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 2006
Accession Number
ADA481946

Entities

People

  • Jonathan N. Blakely
  • Ned J. Corron
  • Scott T. Hayes
  • Shawn D. Pethel

Tags

Communities of Interest

  • Materials and Manufacturing Processes
  • Weapons Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Circuits
  • Data Acquisition
  • Digital Signal Processing
  • Electromagnetic Wave Propagation
  • Electronic Circuits
  • Electronic Components
  • Engineering
  • Filters
  • Frequency
  • Lepidoptera
  • Linear Systems
  • Nonlinear Dynamics
  • Physical Theories
  • Spread Spectrum
  • Wave Propagation
  • Waveforms

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Radar Systems Engineering.

Technology Areas

  • Microelectronics