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Examining the evolution of phase-space elements for C.elegans locomotion.

Dimitrios Tzepos1, Jenny Magnes1

  • 1Vassar College, Department of Physics & Astronomy Poughkeepsie, New York, USA.

Physical Review. E
|April 18, 2026
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Summary

The study reveals Caenorhabditis elegans (C. elegans) locomotion is hyperchaotic, exhibiting two positive Lyapunov exponents. This dynamic behavior, analyzed via phase space, indicates a complex, dissipative system crucial for future modeling.

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Area of Science:

  • * Biophysics and Nonlinear Dynamics
  • * Quantitative Behavioral Analysis
  • * Model Organism Research

Background:

  • * Caenorhabditis elegans (C. elegans) nematodes are established model organisms for behavioral studies.
  • * Dynamic diffraction offers a low-noise method to analyze neuromuscular system dynamics during locomotion.
  • * Understanding locomotion dynamics is key to developing predictive computational models.

Purpose of the Study:

  • * To estimate the Lyapunov spectrum of C. elegans locomotion.
  • * To characterize the underlying dynamical system of nematode movement.
  • * To provide insights for future mathematical and computational modeling of C. elegans behavior.

Main Methods:

  • * Reconstruction of C. elegans locomotion trajectories using Takens embedding.
  • * Estimation of Lyapunov spectra utilizing the Sano-Sawada algorithm.
  • * Verification of spectral results through parameter stability analysis.

Main Results:

  • * Calculation of two positive Lyapunov exponents (0.860±0.028 s⁻¹, 0.389±0.014 s⁻¹) and one negative exponent (-3.451±0.074 s⁻¹).
  • * Identification of C. elegans locomotion as hyperchaotic due to the presence of multiple positive Lyapunov exponents.
  • * Confirmation of a dissipative system, indicated by the negative sum of the Lyapunov exponents.

Conclusions:

  • * C. elegans locomotion exhibits hyperchaotic dynamics, characterized by sensitive dependence on initial conditions.
  • * The nematode's neuromuscular system operates as a dissipative dynamical system.
  • * These findings are significant for advancing mathematical and computational models of biological locomotion.