387 citations · 1.5k across the 33 of their papers we have counts for
6 papers · 2 filters
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 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…
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…