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In this article, on the example of the known low-order dynamical models,namely Lorenz, Rossler and Vallis systems, the difficulties of reliablenumerical analysis of chaotic dynamical systems are discussed. For the Lorenzsystem, the problems of existence of hidden chaotic attractors and hiddentransient chaotic sets and their numerical investigation are considered. Theproblems of the numerical characterization of a chaotic attractor bycalculating finite-time time Lyapunov exponents and finite-time Lyapunovdimension along one trajectory are demonstrated using the example of computingunstable periodic orbits in the Rossler system. Using the example of the Vallissystem describing the El Nino-Southern Oscillation it is demonstrated ananalytical approach for localization of self-excited and hidden attractors,which allows to obtain the exact formulas or estimates of their Lyapunovdimensions.

journal of physics. conference series

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