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

  Kuznetsov, Nikolay; Mokaev, Timur (IOP Publishing, 2019)

  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 ...

• Hidden Strange Nonchaotic Attractors 

  Danca, Marius-F.; Kuznetsov, Nikolay (MDPI AG, 2021)

  In this paper, it is found numerically that the previously found hidden chaotic attractors of the Rabinovich–Fabrikant system actually present the characteristics of strange nonchaotic attractors. For a range of the ...

• D3 Dihedral Logistic Map of Fractional Order 

  Danca, Marius-F.; Kuznetsov, Nikolay (MDPI AG, 2022)

  In this paper, the D3 dihedral logistic map of fractional order is introduced. The map presents a dihedral symmetry D3. It is numerically shown that the construction and interpretation of the bifurcation diagram versus the ...

• The Lorenz system : hidden boundary of practical stability and the Lyapunov dimension 

  Kuznetsov, N. V.; Mokaev, T. N.; Kuznetsova, O. A.; Kudryashova, E. V. (Springer, 2020)

  On the example of the famous Lorenz system, the difficulties and opportunities of reliable numerical analysis of chaotic dynamical systems are discussed in this article. For the Lorenz system, the boundaries of global ...

• Hidden attractors in Chua circuit : mathematical theory meets physical experiments 

  Kuznetsov, Nikolay; Mokaev, Timur; Ponomarenko, Vladimir; Seleznev, Evgeniy; Stankevich, Nataliya; Chua, Leon (Springer Science and Business Media LLC, 2023)

  After the discovery in early 1960s by E. Lorenz and Y. Ueda of the first example of a chaotic attractor in numerical simulation of a real physical process, a new scientific direction of analysis of chaotic behavior in ...