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Updated: Jun 17, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Spectrum of Lyapunov exponents of non-smooth dynamical systems of integrate-and-fire type
Douglas Zhou1, Yi Sun, Aaditya V Rangan
1Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA. zdz@cims.nyu.edu
Abstract:
We discuss how to characterize long-time dynamics of non-smooth dynamical systems, such as integrate-and-fire (I&F) like neuronal network, using Lyapunov exponents and present a stable numerical method for the accurate evaluation of the spectrum of Lyapunov exponents for this large class of dynamics. These dynamics contain (i) jump conditions as in the firing-reset dynamics and (ii) degeneracy such as in the refractory period in which voltage-like variables of the network collapse to a single constant value. Using the networks of linear I&F neurons, exponential I&F neurons, and I&F neurons with adaptive threshold, we illustrate our method and discuss the rich dynamics of these networks.
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