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Related Experiment Video

Updated: Jul 15, 2026

Design and Synthesis of a Reconfigurable DNA Accordion Rack

Design and Synthesis of a Reconfigurable DNA Accordion Rack

Published on: August 15, 2018

Synthesizing folded band chaos.

Ned J Corron¹, Scott T Hayes, Shawn D Pethel

¹U. S. Army RDECOM, AMSRD-AMR-WS-ST, Redstone Arsenal, Alabama 35898, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 16, 2007

Summary

A linear filter can generate both Lorenz-like and Rössler-like chaotic dynamics by altering the random drive encoding. This study reveals connections between source entropy, filter dissipation, and chaos exponents.

Area of Science:

Nonlinear Dynamics
Chaos Theory
Dynamical Systems

Background:

The Lorenz and Rössler systems are canonical examples of chaotic attractors in nonlinear dynamics.
Understanding the underlying mechanisms that generate different chaotic behaviors is crucial for advancing the field.

Purpose of the Study:

To demonstrate that a single randomly driven linear filter can synthesize both Lorenz-like and Rössler-like chaotic waveforms.
To investigate the relationship between the random source's topological entropy, filter dissipation, and the resulting chaotic dynamics.

Main Methods:

Utilizing a randomly driven linear filter architecture.
Employing different encoding schemes for the random driving source.
Analyzing the generated waveforms for characteristics of Lorenz and Rössler attractors.

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Quantifying topological entropy, dissipation, and Lyapunov exponents.

Main Results:

The filter successfully produced Lorenz-like reverse-time chaos with one encoding.
A different encoding resulted in Rössler-like folded band waveforms.
A clear relationship was established between topological entropy, dissipation, and the positive Lyapunov exponent.

Conclusions:

The study unifies Lorenz and Rössler dynamics under a single framework.
Drive encoding acts as a grammar restriction on a general chaotic superset.
This provides a new perspective on the generation and classification of chaotic systems.