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Massive evaluation and analysis of Poincaré recurrences on grids of initial data : A tool to map chaotic diffusion. / Shevchenko, Ivan I.; Rollin, Guillaume; Melnikov, Alexander V.; Lages, José.

в: Computer Physics Communications, Том 246, 106868, 01.2020.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Shevchenko, II, Rollin, G, Melnikov, AV & Lages, J 2020, 'Massive evaluation and analysis of Poincaré recurrences on grids of initial data: A tool to map chaotic diffusion', Computer Physics Communications, Том. 246, 106868. https://doi.org/10.1016/j.cpc.2019.106868

APA

Shevchenko, I. I., Rollin, G., Melnikov, A. V., & Lages, J. (2020). Massive evaluation and analysis of Poincaré recurrences on grids of initial data: A tool to map chaotic diffusion. Computer Physics Communications, 246, [106868]. https://doi.org/10.1016/j.cpc.2019.106868

Vancouver

Shevchenko II, Rollin G, Melnikov AV, Lages J. Massive evaluation and analysis of Poincaré recurrences on grids of initial data: A tool to map chaotic diffusion. Computer Physics Communications. 2020 Янв.;246. 106868. https://doi.org/10.1016/j.cpc.2019.106868

Author

Shevchenko, Ivan I. ; Rollin, Guillaume ; Melnikov, Alexander V. ; Lages, José. / Massive evaluation and analysis of Poincaré recurrences on grids of initial data : A tool to map chaotic diffusion. в: Computer Physics Communications. 2020 ; Том 246.

BibTeX

@article{599f020ff7ec4fd88f20a82244de161e,
title = "Massive evaluation and analysis of Poincar{\'e} recurrences on grids of initial data: A tool to map chaotic diffusion",
abstract = "We present a novel numerical method aimed to characterize global behaviour, in particular chaotic diffusion, in dynamical systems. It is based on an analysis of the Poincar{\'e} recurrence statistics on massive grids of initial data or values of parameters. We concentrate on Hamiltonian systems, featuring the method separately for the cases of bounded and non-bounded phase spaces. The embodiments of the method in each of the cases are specific. We compare the performances of the proposed Poincar{\'e} recurrence method (PRM) and the custom Lyapunov exponent (LE) methods and show that they expose the global dynamics almost identically. However, a major advantage of the new method over the known global numerical tools, such as LE, FLI, MEGNO, and FA, is that it allows one to construct, in some approximation, charts of local diffusion timescales. Moreover, it is algorithmically simple and straightforward to apply.",
keywords = "Celestial mechanics, Dynamical chaos, Dynamical systems, Lyapunov exponents, Numerical methods, Poincar{\'e} recurrences, PLANETS, COMPUTE, STABILITY, Poincare recurrences, MULTIDIMENSIONAL SYSTEMS, MOTION, GLOBAL DYNAMICS, ENTROPY",
author = "Shevchenko, {Ivan I.} and Guillaume Rollin and Melnikov, {Alexander V.} and Jos{\'e} Lages",
year = "2020",
month = jan,
doi = "10.1016/j.cpc.2019.106868",
language = "English",
volume = "246",
journal = "Computer Physics Communications",
issn = "0010-4655",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Massive evaluation and analysis of Poincaré recurrences on grids of initial data

T2 - A tool to map chaotic diffusion

AU - Shevchenko, Ivan I.

AU - Rollin, Guillaume

AU - Melnikov, Alexander V.

AU - Lages, José

PY - 2020/1

Y1 - 2020/1

N2 - We present a novel numerical method aimed to characterize global behaviour, in particular chaotic diffusion, in dynamical systems. It is based on an analysis of the Poincaré recurrence statistics on massive grids of initial data or values of parameters. We concentrate on Hamiltonian systems, featuring the method separately for the cases of bounded and non-bounded phase spaces. The embodiments of the method in each of the cases are specific. We compare the performances of the proposed Poincaré recurrence method (PRM) and the custom Lyapunov exponent (LE) methods and show that they expose the global dynamics almost identically. However, a major advantage of the new method over the known global numerical tools, such as LE, FLI, MEGNO, and FA, is that it allows one to construct, in some approximation, charts of local diffusion timescales. Moreover, it is algorithmically simple and straightforward to apply.

AB - We present a novel numerical method aimed to characterize global behaviour, in particular chaotic diffusion, in dynamical systems. It is based on an analysis of the Poincaré recurrence statistics on massive grids of initial data or values of parameters. We concentrate on Hamiltonian systems, featuring the method separately for the cases of bounded and non-bounded phase spaces. The embodiments of the method in each of the cases are specific. We compare the performances of the proposed Poincaré recurrence method (PRM) and the custom Lyapunov exponent (LE) methods and show that they expose the global dynamics almost identically. However, a major advantage of the new method over the known global numerical tools, such as LE, FLI, MEGNO, and FA, is that it allows one to construct, in some approximation, charts of local diffusion timescales. Moreover, it is algorithmically simple and straightforward to apply.

KW - Celestial mechanics

KW - Dynamical chaos

KW - Dynamical systems

KW - Lyapunov exponents

KW - Numerical methods

KW - Poincaré recurrences

KW - PLANETS

KW - COMPUTE

KW - STABILITY

KW - Poincare recurrences

KW - MULTIDIMENSIONAL SYSTEMS

KW - MOTION

KW - GLOBAL DYNAMICS

KW - ENTROPY

UR - http://www.scopus.com/inward/record.url?scp=85071311224&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/massive-evaluation-analysis-poincar%C3%A9-recurrences-grids-initial-data-tool-map-chaotic-diffusion

U2 - 10.1016/j.cpc.2019.106868

DO - 10.1016/j.cpc.2019.106868

M3 - Article

AN - SCOPUS:85071311224

VL - 246

JO - Computer Physics Communications

JF - Computer Physics Communications

SN - 0010-4655

M1 - 106868

ER -

ID: 45986864