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Updated: May 18, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Extraction of stochastic dynamics from time series
M Petelczyc1, J J Żebrowski, J M Gac
1Faculty of Physics, Warsaw University of Technology, Warsaw, Poland. petelczyc_m@if.pw.edu.pl
Abstract:
We present a method for the reconstruction of the dynamics of processes with discrete time. The time series from such a system is described by a stochastic recurrence equation, the continuous form of which is known as the Langevin equation. The deterministic f and stochastic g components of the stochastic equation are directly extracted from the measurement data with the assumption that the noise has finite moments and has a zero mean and a unit variance. No other information about the noise distribution is needed. This is contrary to the usual Langevin description, in which the additional assumption that the noise is Gaussian (δ-correlated) distributed as necessary. We test the method using one dimensional deterministic systems (the tent and logistic maps) with Gaussian and with Gumbel noise. In addition, results for human heart rate variability are presented as an example of the application of our method to real data. The differences between cardiological cases can be observed in the properties of the deterministic part f and of the reconstructed noise distribution.
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