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Updated: Jan 21, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Decay of the distance autocorrelation and Lyapunov exponents
C F O Mendes1, R M da Silva1, M W Beims1,2
1Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, PR, Brazil.
Abstract:
This work presents numerical evidence that for discrete dynamical systems with one positive Lyapunov exponent the decay of the distance autocorrelation is always related to the Lyapunov exponent. Distinct decay laws for the distance autocorrelation are observed for different systems, namely, exponential decays for the quadratic map, logarithmic for the Hénon map, and power-law for the conservative standard map. In all these cases the decay exponent is close to the positive Lyapunov exponent. For hyperchaotic conservative systems the power-law decay of the distance autocorrelation is not directly related to any Lyapunov exponent.
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