Research output: Contribution to journal › Conference article › peer-review
Numerical analysis of dynamical systems : Unstable periodic orbits, hidden transient chaotic sets, hidden attractors, and finite-time Lyapunov dimension. / Kuznetsov, N. V.; Mokaev, T. N.
In: Journal of Physics: Conference Series, Vol. 1205, No. 1, 012034, 07.05.2019.Research output: Contribution to journal › Conference article › peer-review
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TY - JOUR
T1 - Numerical analysis of dynamical systems
T2 - 7th International Conference Problems of Mathematical Physics and Mathematical Modelling, MPMM 2018
AU - Kuznetsov, N. V.
AU - Mokaev, T. N.
PY - 2019/5/7
Y1 - 2019/5/7
N2 - 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.
AB - 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.
KW - LORENZ
KW - EQUATION
UR - http://www.scopus.com/inward/record.url?scp=85066337391&partnerID=8YFLogxK
UR - http://www.mendeley.com/research/numerical-analysis-dynamical-systems-unstable-periodic-orbits-hidden-transient-chaotic-sets-hidden-a
U2 - 10.1088/1742-6596/1205/1/012034
DO - 10.1088/1742-6596/1205/1/012034
M3 - Conference article
AN - SCOPUS:85066337391
VL - 1205
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
SN - 1742-6588
IS - 1
M1 - 012034
Y2 - 25 June 2018 through 27 June 2018
ER -
ID: 42959299