Data and scripts from: Cycle-expansion method for the Lyapunov exponent, susceptibility, and higher moments

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Lyapunov exponents characterize the chaotic nature of dynamical systems by quantifying the growth rate of uncertainty associated with the imperfect measurement of initial conditions. Finite-time estimates of the exponent, however, experience fluctuations due to both the initial condition and the stochastic nature of the dynamical path. The scale of these fluctuations is governed by the Lyapunov susceptibility, the finiteness of which typically provides a sufficient condition for the law of large numbers to apply. Here, we obtain a formally exact expression for this susceptibility in terms of the Ruelle dynamical zeta function for one-dimensional systems. We further show that, for systems governed by sequences of random matrices, the cycle expansion of the zeta function enables systematic computations of the Lyapunov susceptibility and of its higher-moment generalizations. The method is here applied to a class of dynamical models that maps to static disordered spin chains with interactions stretching over a varying distance, and is tested against Monte Carlo simulations. ... [Read More]

Data Citation

Charbonneau, P., Li, Y. (C.), Pfister, H. D., & Yaida, S. (2017). Cycle-expansion method for the Lyapunov exponent, susceptibility, and higher moments. Duke Digital Repository. https://doi.org/10.7924/G88050N6

Creator: Charbonneau, Patrick
Pfister, Henry D.
Yaida, Sho
Li, Yue (Cathy)
DOI: 10.7924/G88050N6
Subject: Lyapunov exponents
Disordered systems
Information theory
Publication Date: September 15, 2017
ARK: ark:/87924/r4ns0p817
Affiliation: Electrical and Computer Engineering
Chemistry
Physics
Publisher: Duke Digital Repository
Language: eng
Type: Dataset
Format: DAT
ESP
M
TXT
Related Materials: Charbonneau, P., Li, Y. C., Pfister, H. D., & Yaida, S. (2017). Cycle-expansion method for the Lyapunov exponent, susceptibility, and higher moments. Phys. Rev. E, 96, 032129. https://doi.org/10.1103/PhysRevE.96.032129
Contact: Patrick Charbonneau: patrick.charbonneau@duke.edu, ORCID: 0000-0001-7174-0821
License: Creative Commons CC0 1.0 Universal
Title: Data and scripts from: Cycle-expansion method for the Lyapunov exponent, susceptibility, and higher moments
License: http://creativecommons.org/publicdomain/zero/1.0/
Repository: Duke Research Data Repository

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Data and generating script for Figure1a	2018-09-10	Public
Data and generating script for Figure3b	2018-09-10	Public
Data and generating script for Figure4a	2018-09-10	Public
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Data and generating script for Figure1c	2018-09-10	Public
Data and generating script for Figure3a	2018-09-10	Public
Data and generating script for Figure1d	2018-09-10	Public
Data and generating script for Figure1b	2018-09-10	Public
Data and generating script for Figure3c	2018-09-10	Public

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