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Updated: May 10, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Joint distribution of first exit times of a two dimensional Wiener process with jumps with application to a pair of
Laura Sacerdote1, Cristina Zucca
1Department of Mathematics G. Peano, University of Torino, Via Carlo Alberto 10, Turin, Italy. laura.sacerdote@unito.it
Abstract:
Motivated by a neuronal modeling problem, a bivariate Wiener process with two independent components is considered. Each component evolves independently until one of them reaches a threshold value. If the first component crosses the threshold value, it is reset while the dynamics of the other component remains unchanged. But, if this happens to the second component, the first one has a jump of constant amplitude; the second component is then reset to its starting value and its evolution restarts. Both processes evolve once again until one of them reaches again its boundary. In this work, the coupling of the first exit times of the two connected processes is studied.
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