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Unstable periodic orbits and noise in chaos computing.
Behnam Kia1, Anna Dari, William L Ditto
1School of Biological and Health Systems Engineering, Arizona State University, Tempe, Arizona 85287-9709, USA.
Chaos (Woodbury, N.Y.)
|January 10, 2012
Summary
This study uses unstable periodic orbits from chaotic systems to create noise-robust models for chaos computing. These models are crucial for biological applications where noise is prevalent and exact equations are unavailable.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Computational Science
Background:
- Chaotic systems offer complex patterns for computation and communication.
- Instability in chaotic systems necessitates careful consideration of noise robustness for computation.
Purpose of the Study:
- To develop models for chaotic systems using unstable periodic orbits.
- To measure orbit sensitivity to noise and select noise-robust symbolic representations.
- To extract periodic orbit-based models from time series data.
Main Methods:
- Utilizing unstable periodic orbits as the fundamental structure of chaotic systems.
- Developing models to quantify the noise sensitivity of individual orbits.
- Employing time series analysis techniques for model extraction.
Main Results:
- Identification of specific unstable periodic orbits with symbolic representations robust to noise.
- Demonstration that periodic orbit-based models can be extracted from time series.
- Establishment of a framework for analyzing noise effects in chaos-based computations.
Conclusions:
- Unstable periodic orbits provide a viable skeleton for building noise-robust chaos computing models.
- Time series extraction methods are critical for applying chaos computing to systems like biological ones.
- The developed models are essential for understanding and mitigating noise in biological chaos implementations.
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