Massive evaluation and analysis of Poincaré recurrences on grids of initial data: A tool to map chaotic diffusion

Ivan I. Shevchenko, Guillaume Rollin, Alexander V. Melnikov, José Lages

Результат исследований: Научные публикации в периодических изданияхстатья

Выдержка

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.

Язык оригиналаанглийский
Номер статьи106868
ЖурналComputer Physics Communications
DOI
СостояниеОпубликовано - 2019

Отпечаток

grids
exponents
Hamiltonians
Lyapunov methods
evaluation
charts
dynamical systems
Numerical methods
Dynamical systems
Statistics
statistics
approximation

Предметные области Scopus

  • Аппаратное обеспечение и архитектура ЭВМ
  • Физика и астрономия (все)

Цитировать

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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",
author = "Shevchenko, {Ivan I.} and Guillaume Rollin and Melnikov, {Alexander V.} and Jos{\'e} Lages",
year = "2019",
doi = "10.1016/j.cpc.2019.106868",
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journal = "Computer Physics Communications",
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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, 2019.

Результат исследований: Научные публикации в периодических изданияхстатья

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 - 2019

Y1 - 2019

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

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