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 -