387 citations · 1.5k across the 33 of their papers we have counts for
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A Survey on Dynamic Analysis of the Costas Loop
R. E. Best, N. V. Kuznetsov, G. A. Leonov +2
This survey is devoted to the dynamic analysis of the Costas loop. In particular the acquisition process is analyzed in great detail. Acquision is most conventiently described by a…
Lyapunov dimension formula of attractors in the Tigan and Yang systems
G. A. Leonov, N. V. Kuznetsov, N. A. Korzhemanova +1
In latter days the technique of attractors dimension estimate of Lorenz type systems is actively developed. In this work the Lyapunov dimension of attractors of the Tigan and Yang…
A short survey on Lyapunov dimension for finite dimensional dynamical systems in Euclidean space
G. A. Leonov, N. V. Kuznetsov
Nowadays there are a number of surveys and theoretical works devoted to the Lyapunov exponents and Lyapunov dimension, however most of them are devoted to infinite dimensional syst…
The Lyapunov dimension and its computation for self-excited and hidden attractors in the Glukhovsky-Dolzhansky fluid convection model
N. V. Kuznetsov, G. A. Leonov, T. N. Mokaev
Consideration of various hydrodynamic phenomena involves the study of the Navier-Stokes (N-S) equations, what is hard enough for analytical and numerical investigations since alrea…
The Lyapunov dimension formula for the global attractor of the Lorenz system
G. A. Leonov, N. V. Kuznetsov, N. A. Korzhemanova +1
The exact Lyapunov dimension formula for the Lorenz system has been analytically obtained first due to G.A.Leonov in 2002 under certain restrictions on parameters, permitting class…
Limitations of the classical phase-locked loop analysis
N. V. Kuznetsov, O. A. Kuznetsova, G. A. Leonov +3
Nonlinear analysis of the classical phase-locked loop (PLL) is a challenging task. In classical engineering literature simplified mathematical models and simulation are widely used…
A dynamical model of Sayano-Shushenskaya hydropower plant: stability, oscillations, and accident
G. A. Leonov, N. V. Kuznetsov, E. P. Solovyeva
This work is devoted to the construction and study of a mathematical model of hydropower unit, consisting of synchronous generator, hydraulic turbine, and speed governor. It is mot…
Limitations of PLL simulation: hidden oscillations in MatLab and SPICE
G. Bianchi, N. V. Kuznetsov, G. A. Leonov +2
Nonlinear analysis of the phase-locked loop (PLL) based circuits is a challenging task, thus in modern engineering literature simplified mathematical models and simulation are wide…
Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion
G. A. Leonov, N. V. Kuznetsov, T. N. Mokaev
In this tutorial, 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…
A short survey on nonlinear models of the classic Costas loop: rigorous derivation and limitations of the classic analysis
R. E. Best, N. V. Kuznetsov, O. A. Kuznetsova +3
Rigorous nonlinear analysis of the physical model of Costas loop --- a classic phase-locked loop (PLL) based circuit for carrier recovery, is a challenging task. Thus for its analy…
Hold-in, pull-in, and lock-in ranges of PLL circuits: rigorous mathematical definitions and limitations of classical theory
G. A. Leonov, N. V. Kuznetsov, M. V. Yuldashev +1
The terms hold-in, pull-in (capture), and lock-in ranges are widely used by engineers for the concepts of frequency deviation ranges within which PLL-based circuits can achieve loc…
Estimation of Lyapunov dimension for the Chen and Lu systems
G. A. Leonov, N. V. Kuznetsov, N. A. Korzhemanova +1
Nowadays various estimates of Lyapunov dimension of Lorenz-like systems attractors are actively developed. Within the frame of this study the question arises whether it is possible…
Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system
N. V. Kuznetsov, G. A. Leonov, T. N. Mokaev +2
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…