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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

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Published on: September 23, 2025

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.

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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.