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Updated: Jul 15, 2026

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

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

Published on: September 23, 2025

Resonant forcing of multidimensional chaotic map dynamics.

Glenn Foster¹, Alfred W Hübler, Karin Dahmen

¹Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.

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

|May 16, 2007

Summary

Researchers identified optimal forcing functions for chaotic dynamics. These resonant functions conserve trajectory displacement and mirror the system

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Area of Science:

Nonlinear dynamics
Chaos theory
Statistical mechanics

Background:

Chaotic systems exhibit sensitive dependence on initial conditions.
Understanding and controlling chaotic behavior is a key challenge in nonlinear dynamics.

Purpose of the Study:

To determine the additive forcing function that elicits the largest response in chaotic map dynamics.
To analyze the properties and effectiveness of resonant forcing functions.

Main Methods:

Utilizing the calculus of variations to derive the optimal forcing function.
Analyzing the relationship between forcing functions and trajectory separation.
Comparing optimal forcing with random forcing.

Main Results:

Resonant forcing functions conserve the product of trajectory displacement and forcing.
The periodicity of resonant forcing matches that of displacement dynamics.
Resonant forcing functions decrease exponentially at a rate determined by the largest Lyapunov exponent.

Conclusions:

Optimal resonant forcing is highly effective when the largest Lyapunov exponent dominates.
For very large Lyapunov exponents, optimal forcing effectiveness diminishes, approaching that of single-push forcing.