Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion: Homoclinic orbits, and self-excited and hidden …

GA Leonov, NV Kuznetsov, TN Mokaev - The European Physical Journal …, 2015 - Springer
In this paper, we discuss self-excited and hidden attractors for systems of differential
equations. We considered the example of a Lorenz-like system derived from the well-known …

Hidden attractors in dynamical systems. From hidden oscillations in Hilbert–Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits

GA Leonov, NV Kuznetsov - International Journal of Bifurcation and …, 2013 - World Scientific
From a computational point of view, in nonlinear dynamical systems, attractors can be
regarded as self-excited and hidden attractors. Self-excited attractors can be localized …

Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system

NV Kuznetsov, GA Leonov, TN Mokaev, A Prasad… - Nonlinear …, 2018 - Springer
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 …

Hidden attractors in dynamical systems: systems with no equilibria, multistability and coexisting attractors

NV Kuznetsov, GA Leonov - IFAC Proceedings Volumes, 2014 - Elsevier
From a computational point of view it is natural to suggest the classification of attractors,
based on the simplicity of finding basin of attraction in the phase space: an attractor is called …

Rare and hidden attractors in Van der Pol-Duffing oscillators

S Brezetskyi, D Dudkowski, T Kapitaniak - The European Physical Journal …, 2015 - Springer
We study the dynamics of the single and coupled van der Pol-Duffing oscillators. Each
oscillator is characterized by the multistability (the coexistence of attractors). Some of the …

Cost function based on Gaussian mixture model for parameter estimation of a chaotic circuit with a hidden attractor

SK Lao, Y Shekofteh, S Jafari… - International Journal of …, 2014 - World Scientific
In this paper, we introduce a new chaotic system and its corresponding circuit. This system
has a special property of having a hidden attractor. Systems with hidden attractors are newly …

Prediction of hidden oscillations existence in nonlinear dynamical systems: Analytics and simulation

GA Leonov, NV Kuznetsov - … 2013: Prediction, Modeling and Analysis of …, 2013 - Springer
From a computational point of view, in nonlinear dynamical systems, attractors can be
regarded as self-excited and hidden attractors. Self-excited attractors can be localized …

Hidden oscillations in drilling system actuated by induction motor

MA Kiseleva, NV Kuznetsov, GA Leonov… - IFAC Proceedings …, 2013 - Elsevier
Study of drilling systems is a topical problem in drilling industry due to the amount of failures
which lead to considerable cost and time loses for mining companies. This paper presents …

Hidden oscillations in drilling systems: torsional vibrations

GA Leonov, MA Kiseleva, NV Kuznetsov… - Journal of Applied …, 2013 - elibrary.ru
Study of drilling systems plays important role in drilling industry. During the operation mode
these systems experience different kinds of vibration, which may cause malfunctioning (ie …

IWCFTA2012 Keynote speech I-Hidden attractors in dynamical systems: From hidden oscillation in Hilbert-Kolmogorov, Aizerman and Kalman problems to hidden …

GA Leonov, NV Kuznetsov - 2012 Fifth International Workshop …, 2012 - ieeexplore.ieee.org
Summary form only given. In this survey an attempt is made to reflect the current trends in
the synthesis of analytical and numerical methods to develop efficient analytical-numerical …