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List of works by Nikolay Kuznetsov

A Tribute to J. C. Sprott

scientific article

A comparison theorem for super- and subsolutions of $\mathbf {\nabla ^2 u + f (u) = 0}$ and its application to water waves with vorticity

scientific article published in 2019

A direct method for calculating Lyapunov quantities of two-dimensional dynamical systems

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A novel memristive time–delay chaotic system without equilibrium points

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A short survey on Pyragas time-delay feedback stabilization and odd number limitation

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A short survey on nonlinear models of QPSK Costas loop

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A short survey on nonlinear models of the classic Costas loop: Rigorous derivation and limitations of the classic analysis

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A simple dynamical model of hydropower plant: stability and oscillations

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ALGORITHM FOR CALCULATING TRANSIENTS IN ELECTRICAL CIRCUITS BY THE STATE-VARIABLE METHOD

scientific article published in 2022

ANALYSIS OF PHASE-LOCKED SYSTEMS WITH DISCONTINUOUS CHARACTERISTICS

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Adaptive synapse-based neuron model with heterogeneous multistability and riddled basins

scientific article published in December 2022

Aircraft control with anti-windup compensation

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Aircraft wing rock oscillations suppression by simple adaptive control

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Algorithm for constructing counterexamples to the Kalman problem

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Algorithm for construction of counterexamples to Aizerman's and Kalman's conjectures*

scientific article published in 2010

Algorithm for localizing Chua attractors based on the harmonic linearization method

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Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua’s circuits

scholarly article by V. O. Bragin et al published August 2011 in Journal of Computer and Systems Sciences International

Algorithms for searching for hidden oscillations in the Aizerman and Kalman problems

scientific article (publication date: August 2011)

Analysis of oscillations in discontinuous Lurie systems via LPRS method

Analytic Exact Upper Bound for the Lyapunov Dimension of the Shimizu–Morioka System

article by Gennady Leonov et al published 22 July 2015 in Entropy

Analytical Method for Computation of Phase-Detector Characteristic

Analytical methods for computation of phase-detector characteristics and PLL design

Analytical-Numerical Localization of Hidden Attractor in Electrical Chua’s Circuit

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Analytical-Numerical Methods for Hidden Attractors’ Localization: The 16th Hilbert Problem, Aizerman and Kalman Conjectures, and Chua Circuits

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Analytical-numerical analysis of closed-form dynamic model of Sayano-Shushenskaya hydropower plant: stability, oscillations, and accident

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Analytical-numerical methods for investigation of hidden oscillations in nonlinear control systems

Approximating hidden chaotic attractors via parameter switching.

scientific article published in January 2018

Attractor as a convex combination of a set of attractors

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BPSK Costas loop: Simulation of nonlinear models in MatLab Simulink

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Best's conjecture on pull-in range of two-phase Costas loop

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Chaos and Its Degradation-Promoting-Based Control in an Antithetic Integral Feedback Circuit

Chaos control in the fractional order logistic map via impulses

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Chimera states and hidden attractors: Comment on "Chimera states in neuronal networks: A review" by S. Majhi, B.K. Bera, D. Ghosh, M. Perc

scientific article published on 25 February 2019

Chimera states in a class of hidden oscillatory networks

Coexistence of hidden attractors and multistability in counterexamples to the Kalman conjecture

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Coexistence of single- and multi-scroll chaotic orbits in a single-link flexible joint robot manipulator with stable spiral and index-4 spiral repellor types of equilibria

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Coincidence of the Gelig–Leonov–Yakubovich, Filippov, and Aizerman–Pyatnitskiy definitions

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Complex dynamics, hidden attractors and continuous approximation of a fractional-order hyperchaotic PWC system

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Computation of lock-in range for classic PLL with lead-lag filter and impulse signals

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Computation of phase detector characteristics in synchronization systems

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Computation of the lock-in ranges of phase-locked loops with PI filter

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Computation of the phase detector characteristic of a QPSK Costas loop

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Computation of the phase detector characteristic of classical PLL

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Computational Experiments with the Roots of Fibonacci-like Polynomials as a Window to Mathematics Research

scientific article published in 2022

Control of multistability in hidden attractors

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Control of pneumatically actuated 6-DOF Stewart platform for driving simulator

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Controlling Dynamics of Hidden Attractors

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Convergence based anti-windup design method and its application to flight control

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Convergence-based Analysis of Robustness to Delay in Anti-windup Loop of Aircraft Autopilot∗∗This work was supported by Russian Scientific Foundation (project 14-21-00041) and Saint-Petersburg State University

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Counterexamples to the Kalman Conjectures

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Coupled Discrete Fractional-Order Logistic Maps

Cycles of two-dimensional systems: Computer calculations, proofs, and experiments

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D3 Dihedral Logistic Map of Fractional Order

scholarly article published 20 December 2021

D3 Dihedral Logistic Map of Fractional Order

scientific article published on 11 January 2022

Delayed feedback stabilization and the Huijberts–Michiels–Nijmeijer problem

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Differential equations of Costas loop

Discontinuous differential equations: comparison of solution definitions and localization of hidden Chua attractors

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Drilling systems failures and hidden oscillations

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Drillstring-hole calculation in drilling simulator

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Dynamics and control of the Stewart platform

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Dynamics of a Stewart platform

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Dynamics of the Shapovalov mid-size firm model

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Dynamics of the Zeraoulia–Sprott Map Revisited

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Elegant analytic computation of phase detector characteristic for non-sinusoidal signals

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Elegant computation of phase-detector characteristics of BPSK Costas loop with non-sinusoidal signals

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Erratum: On the two-dimensional sloshing problem

scientific article published in August 2011

Existence of homoclinic orbits and heteroclinic cycle in a class of three-dimensional piecewise linear systems with three switching manifolds

scientific article published on 01 December 2020

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

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Fractional-order PWC systems without zero Lyapunov exponents

Generating grid chaotic sea from system without equilibrium point

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Global Problems for Differential Inclusions. Kalman and Vyshnegradskii Problems and Chua Circuits

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Graphical Structure of Attraction Basins of Hidden Chaotic Attractors: The Rabinovich–Fabrikant System

Harmonic Balance Method and Stability of Discontinuous Systems

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Harmonic balance analysis of pull-in range and oscillatory behavior of third-order type 2 analog PLLs

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Harmonic balance method, Tsypkin locus, and LPRS: comparison and counterexamples

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Hidden Attractors in Fundamental Problems and Engineering Models: A Short Survey

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Hidden Attractors on One Path: Glukhovsky–Dolzhansky, Lorenz, and Rabinovich Systems

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Hidden Nonlinear Oscillations in Controlled Aircraft With Saturated Inputs

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Hidden Oscillations In The Closed-Loop Aircraft-Pilot System And Their Prevention* *This work was supported by Russian Science Foundation (project 14-21-00041) and Saint-Petersburg State University

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Hidden Oscillations in Drilling Systems: Torsional Vibrations

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Hidden Oscillations in Dynamical Systems. 16 Hilbert’s Problem, Aizerman’s and Kalman’s Conjectures, Hidden Attractors in Chua’s Circuits

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Hidden Strange Nonchaotic Attractors

Hidden and self-excited attractors in Chua circuit: synchronization and SPICE simulation

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Hidden attractor and homoclinic orbit in Lorenz-like system describing convective fluid motion in rotating cavity

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Hidden attractor in smooth Chua systems

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Hidden attractor in the Rabinovich system, Chua circuits and PLL

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Hidden attractors and multistability in a modified Chua’s circuit

Hidden attractors in Chua circuit: mathematical theory meets physical experiments

scientific article published on 21 December 2022

Hidden attractors in dynamical systems

Hidden attractors in electromechanical systems with and without equilibria

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Hidden attractors localization in Chua circuit via the describing function method

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Hidden chaotic sets in a Hopfield neural system

Hidden nonlinear oscillations in aircraft stabilization system with restrictions at the actuator control

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Hidden oscillations in SPICE simulation of two-phase Costas loop with non-linear VCO

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Hidden oscillations in aircraft flight control system with input saturation

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Hidden oscillations in drilling system actuated by induction motor

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Hidden oscillations in drilling systems with salient pole synchronous motor

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Hidden oscillations in mathematical model of drilling system actuated by induction motor with a wound rotor

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Hidden oscillations in nonlinear control systems

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Hold-In, Pull-In, and Lock-In Ranges of PLL Circuits: Rigorous Mathematical Definitions and Limitations of Classical Theory

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Hold-in, Pull-in and Lock-in Ranges for Phase-locked Loop with Tangential Characteristic of the Phase Detector

Homoclinic Bifurcations and Chaos in the Fishing Principle for the Lorenz-like Systems

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

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Identification of Human Model Parameters for the Human-Machine Control Systems Design

scientific article published on 17 May 2022

Impact of chaotic dynamics on the performance of metaheuristic optimization algorithms: An experimental analysis

In Memoriam: Gennady Alekseevich Leonov

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Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations ⬇️

Jacobi Stability Analysis and the Onset of Chaos in a Two-Degree-of-Freedom Mechanical System

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Limit cycles of quadratic systems with a perturbed weak focus of order 3 and a saddle equilibrium at infinity

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Limitations of PLL simulation: Hidden oscillations in MatLab and SPICE

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Limitations of the classical phase-locked loop analysis

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Localization of hidden Chuaʼs attractors

scientific article (publication date: June 2011)

Localization of hidden attractors of the generalized Chua system based on the method of harmonic balance

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Localization of hidden oscillations in flight control systems

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Localization of the attractor of the differential equations for the solar wind-magnetosphere-ionosphere model

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Lock-in range of BPSK Costas loop

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Looking More Closely at the Rabinovich–Fabrikant System

Lyapunov dimension formula for the global attractor of the Lorenz system ⬇️

scientific article (publication date: December 2016)

Mathematical modeling of vibrations in turbogenerator sets of Sayano-Shushenskaya Hydroelectric Power Station

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Mathematical models of the Costas loop

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Matlab Code for Lyapunov Exponents of Fractional-Order Systems

Metaharmonic functions: Mean flux theorem, its converse and related properties

scientific article published in 2022

Methods for suppressing nonlinear oscillations in astatic auto-piloted aircraft control systems

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Model-free prediction of multistability using echo state network

scientific article published in October 2022

Modeling and identification of the Tunisian social system in 2011-2014: bifurcation, revolution, and controlled stabilization

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Modeling, Simulation and Control of Pneumatically Actuated Stewart Platform with Input Quantization

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Motion of a solid driven by six rods of variable length

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Multistability and Hidden Attractors in the Dynamics of Permanent Magnet Synchronous Motor

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New adaptive synchronization algorithm for a general class of complex hyperchaotic systems with unknown parameters and its application to secure communication

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Non-linear analysis of a modified QPSK Costas loop

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Nonlinear Analysis of Charge-Pump Phase-Locked Loop: The Hold-In and Pull-In Ranges

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Nonlinear Phase Shift Compensator for Pilot-Induced Oscillations Prevention

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Nonlinear analysis of PLL by the harmonic balance method: limitations of the pull-in range estimation

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Nonlinear analysis of phase-locked loop with squarer

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Nonlinear dynamical model of Costas loop and an approach to the analysis of its stability in the large

Nonlinear mathematical models of Costas Loop for general waveform of input signal

Nonlinear model of the optical Costas loop: pull-in range estimation and hidden oscillations

Nonlinear problems in control of manufacturing systems

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

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Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor

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On Flutter Suppression in the Keldysh Model

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On Leonov’s Method for Computing the Linearization of Transverse Dynamics and Analyzing Zhukovsky Stability

scientific article published in October 2019

On asymmetric periodic solutions in relay feedback systems

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On counter-examples to Aizerman and Kalman conjectures

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On differences and similarities in the analysis of Lorenz, Chen, and Lu systems ⬇️

scientific article (publication date: April 2015)

On lower-bound estimates of the Lyapunov dimension and topological entropy for the Rossler systems

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On problems of Aizerman and Kalman

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On stability by the first approximation for discrete systems

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On the Gardner Problem for Phase-Locked Loops

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On the Gardner Problem for the Phase-Locked Loops

scientific article published in 2019

On the Generalized Gardner Problem for Phase-Locked Loops in Electrical Grids

scientific article published in May 2021

On the Keldysh problem of flutter suppression

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On the Stability of Nonlinear Systems with the Monotonic Differentiable Nonlinear Characteristics

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Optimal control and genetic algorithms in modeling dynamical allocation of resources for a three-sector economy

scientific article published on 10 November 2022

Oscillations in pulse-width modulated system

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Parameter Switching Synchronization

scholarly article by MARIUS-F. DANCA & Nikolay Kuznetsov published November 2017 in Applied Mathematics and Computation

Pattern generation in diffusive networks: How do those brainless centipedes walk?

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Pilot-Induced Oscillations and Their Prevention

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Poincaré series and an extension of the Lehmer conjecture

scientific article published in 1985

Prediction of Hidden Oscillations Existence in Nonlinear Dynamical Systems: Analytics and Simulation

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Pull-in range of the PLL-based circuits with proportionally-integrating filter∗∗This work was supported by Saint-Petersburg State University (project 6.39.416.2014, s. 3-4; project 6.38.505.2014, s. 5.). and Russian Scientific Foundation (project

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Pull-in range of the classical PLL with impulse signals

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Response of Costas PLL in the Presence of In-band Interference

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Rich dynamics and anticontrol of extinction in a prey–predator system

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Rigorous mathematical definitions of the hold-in and pull-in ranges for phase-locked loops

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SYNCHRONIZATION OF TWO METRONOMES

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Saddle-node bifurcation of periodic orbit route to hidden attractors

scientific article published in 2023

Scenario of the Birth of Hidden Attractors in the Chua Circuit

Serial Nonlinear Correction Method in the Flight Vehicle Systems

scientific article published in 2023

Shadowing in hidden attractors

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Simulation of Analog Costas Loop Circuits

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Simulation of PLL with impulse signals in MATLAB: Limitations, hidden oscillations, and pull-in range

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Simulation of movements of heavy mining shovels

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Simulation of nonlinear models of QPSK costas loop in MatLab Simulink

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Simulation of nonlinear models of modified BPSK Costas loop for non sinusoidal waveforms in MatLab Simulink

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Simulation of phase-locked loops in phase-frequency domain

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Simulation of the classical analog phase-locked loop based circuits

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Stability and Chaotic Attractors of Memristor-Based Circuit with a Line of Equilibria

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Stability domain analysis of an antiwindup control system for an unstable object

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Stability of charge-pump phase-locked loops: the hold-in and pull-in ranges

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Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents

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Suppression of nonlinear wing-rock oscillations by adaptive control with the implicit reference model

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Switching algorithm for data fusion of small low-cost UAV navigation system*

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Synchronization of Hidden Hyperchaotic Attractors in Fractional-Order Complex-Valued Systems with Application to Secure Communications

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Synchronization of hidden chaotic attractors on the example of radiophysical oscillators

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The Egan Problem on the Pull-in Range of Type 2 PLLs

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The Gardner Problem and Cycle Slipping Bifurcation for Type-2 Phase-Locked Loops

scientific article published in July 2022

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

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The Lyapunov dimension and its estimation via the Leonov method ⬇️

The birth of the global stability theory and the theory of hidden oscillations

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The floating-body problem: an integro-differential equation without irregular frequencies

scientific article published in 2020

The pull-in range and a counterexample to the Egan conjecture for the fourth-order type 2 analog PLL

scientific article published in 2021

Theory of Differential Inclusions and Its Application in Mechanics

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Time varying feedback control on multi-stability in hidden attractor

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Time-delay control for stabilization of the Shapovalov mid-size firm model

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Tunisia 2011–2014. Bifurcation, revolution, and controlled stabilization

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Tutorial on dynamic analysis of the Costas loop ⬇️

UAV control with switched GNSS-Estimator navigation system∗∗This work was supported by Russian Scientific Foundation (project 14-21-00041) and Saint-Petersburg State University

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Unusual dynamics and hidden attractors of the Rabinovich–Fabrikant system

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V. A. Yakubovich -mathematician, "father of the field", and herald of intellectual democracy in science and society∗1See also obituaries published by IFAC (Leonov and Kurzhanski, 2012) and IEEE (Fradkov et al., 2013)

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Visualization of Four Normal Size Limit Cycles in Two-Dimensional Polynomial Quadratic System

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