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Updated: Nov 29, 2025

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Statistics of residence time for Lévy flights in unstable parabolic potentials
Alexander A Dubkov1, Bartłomiej Dybiec2, Bernardo Spagnolo1,3,4
1Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, Gagarin Avenue 23, 603950 Nizhni Novgorod, Russia.
Abstract:
We analyze the residence time problem for an arbitrary Markovian process describing nonlinear systems without a steady state. We obtain exact analytical results for the statistical characteristics of the residence time. For diffusion in a fully unstable potential profile in the presence of Lévy noise we get the conditional probability density of the particle position and the average residence time. The noise-enhanced stability phenomenon is observed in the system investigated. Results from numerical simulations are in very good agreement with analytical ones.
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