Numerical analysis of dynamical systems: Unstable periodic orbits, hidden transient chaotic sets, hidden attractors, and finite-time Lyapunov dimension

Результат исследований: Научные публикации в периодических изданияхстатья в журнале по материалам конференции

13 Цитирования (Scopus)

Аннотация

In this article, on the example of the known low-order dynamical models, namely Lorenz, Rössler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz system, the problems of existence of hidden chaotic attractors and hidden transient chaotic sets and their numerical investigation are considered. The problems of the numerical characterization of a chaotic attractor by calculating finite-time time Lyapunov exponents and finite-time Lyapunov dimension along one trajectory are demonstrated using the example of computing unstable periodic orbits in the Rössler system. Using the example of the Vallis system describing the El Ninõ-Southern Oscillation it is demonstrated an analytical approach for localization of self-excited and hidden attractors, which allows to obtain the exact formulas or estimates of their Lyapunov dimensions.

Язык оригиналаанглийский
Номер статьи012034
ЖурналJournal of Physics: Conference Series
Том1205
Номер выпуска1
DOI
СостояниеОпубликовано - 7 мая 2019
Событие7th International Conference Problems of Mathematical Physics and Mathematical Modelling, MPMM 2018 - Moscow, Российская Федерация
Продолжительность: 25 июн 201827 июн 2018

Предметные области Scopus

  • Физика и астрономия (все)

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