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A simple Lorenz circuit and its radio frequency implementation.

Jonathan N Blakely1, Michael B Eskridge, Ned J Corron

  • 1U.S. Army Research, Development, and Engineering Command, AMSRD-AMR-WS-ST, Redstone Arsenal, Alabama 35898, USA.

Chaos (Woodbury, N.Y.)
|July 7, 2007
PubMed
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A novel electronic circuit based on the chaotic Lorenz system was developed using minimal components. This simple design demonstrates classic chaotic behavior and is suitable for radio frequency applications.

Area of Science:

  • Chaos theory
  • Electronic circuit design
  • Nonlinear dynamics

Background:

  • The Lorenz system is a fundamental model in chaos theory, known for its complex dynamics.
  • Implementing chaotic systems in electronic circuits can be challenging due to component requirements.

Purpose of the Study:

  • To design and experimentally verify a simplified electronic circuit that emulates the chaotic Lorenz system.
  • To assess the suitability of this circuit for practical applications, particularly in radio frequency (RF) domains.

Main Methods:

  • The circuit was designed using only two active nonlinear elements (high-speed analog multipliers) and passive linear components.
  • Experimental implementations were conducted to observe the circuit's behavior.
  • Power spectrum analysis was performed to characterize the frequency output.

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Main Results:

  • The circuit successfully exhibited the characteristic butterfly attractor of the Lorenz system.
  • Hysteretic transitions from steady state to chaos were observed, matching theoretical predictions.
  • The circuit demonstrated significant power output up to 930 kHz, with notable power extending beyond 1 MHz.

Conclusions:

  • A remarkably simple and effective electronic circuit for generating Lorenz chaos has been demonstrated.
  • The circuit's simplicity and performance make it a promising candidate for RF applications.
  • This work validates the feasibility of creating complex chaotic dynamics with minimal electronic components.