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Updated: Jun 21, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Stochastic hierarchical systems: excitable dynamics
Helmar Leonhardt1, Michael A Zaks, Martin Falcke
1Institute of Physics, Humboldt University at Berlin, Newtonstr. 15, D-12489, Berlin, Germany, helmar_leonhardt@web.de.
Abstract:
We present a discrete model of stochastic excitability by a low-dimensional set of delayed integral equations governing the probability in the rest state, the excited state, and the refractory state. The process is a random walk with discrete states and nonexponential waiting time distributions, which lead to the incorporation of memory kernels in the integral equations. We extend the equations of a single unit to the system of equations for an ensemble of globally coupled oscillators, derive the mean field equations, and investigate bifurcations of steady states. Conditions of destabilization are found, which imply oscillations of the mean fields in the stochastic ensemble. The relation between the mean field equations and the paradigmatic Kuramoto model is shown.
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