• Corpus ID: 235490429

# Analytical and numerical study of the hidden boundary of practical stability: complex versus real Lorenz systems

@inproceedings{Kuznetsov2021AnalyticalAN,
title={Analytical and numerical study of the hidden boundary of practical stability: complex versus real Lorenz systems},
author={Nikolay V. Kuznetsov and Timur N. Mokaev and A. A.-H. Shoreh and Awadesh Prasad and Manish Dev Shrimali},
year={2021}
}
• Published 20 June 2021
• Materials Science
N.V. Kuznetsov, 2, 3, ∗ T.N. Mokaev, A.A.-H. Shoreh, 4 A. Prasad, and M.D. Shrimali Faculty of Mathematics and Mechanics, St. Petersburg State University, Peterhof, St. Petersburg, Russia Faculty of Information Technology, University of Jyväskylä, Jyväskylä, Finland Institute for Problems in Mechanical Engineering RAS, Russia Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt Department of Physics & Astrophysics, Delhi University, India Central University of…

## References

SHOWING 1-10 OF 56 REFERENCES

• Physics
Nonlinear Dynamics
• 2020
The difficulties and opportunities of reliable numerical analysis of chaotic dynamical systems are discussed and the Lyapunov dimension of attractors via the Pyragas time-delayed feedback control technique and the Leonov method is demonstrated.
>In the study of the stability of a system, it is never completely satisfactory to know only that an equilibrium state is asymptotically stable. As a practical matter, it is necessary to have some
• N. Kuznetsov
• Mathematics
Journal of Computer and Systems Sciences International
• 2020
This survey discusses well-known theoretical and engineering problems in which hidden oscillations (their absence or presence and location) play an important role.
Interest in the field of non-linear differential equations in bygone years centered around the dynamics of conservative systems, the problems arising mainly in celestial mechanics. Current interest
• Physics
• 2015
The Rabinovich system, describing the process of interaction between waves in plasma, is considered. It is shown that the Rabinovich system can exhibit a hidden attractor in the case of
• Mathematics
2020 European Control Conference (ECC)
• 2020
A brief history of the first global stability criteria development and corresponding counterexamples with hidden oscillations are discussed and boundaries of global stability in the space of parameters are limited by the birth of oscillations.
• Physics
• 2017
Abstract In this paper, the classic Lorenz system is revisited. Some dynamical behaviors are shown with the Rayleigh number ρ$\rho$ somewhat smaller than the critical value 24.06 by studying the
§ 4 Determining Functionals for Abstract Semilinear Parabolic Equations In this section we prove a number of assertions on the existence and properties of determining functionals for processes