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Prof. Kuznetsov’s research interests are in dynamical systems and applied mathematics. In his works, a combination of rigorous analytical and reliable numerical methods allowed for both the advancement in solving previously known fundamental unsolved problems as well as the development of modern engineering technologies. Among his main results are the development of the theory of hidden oscillations and the concept of self-excited and hidden attractors, the discovery of a hidden Chua attractor in Chua circuits,[7] revealing of coexisting hidden attractors in electomechanical models with Sommerfeld effect, solutions to the Egan problem on the pull-in range and to the Gardner problem on the lock-in range for phase-locked loops, nonlinear analysis of the CP-PLL and validation of the Gardner conjecture, counterexamples with self-excited and hidden attractors to the classical describing function method, developed effective analytical-numerical methods for the construction of counterexamples to the Kalman conjecture on the absolute stability of control systems, provided justification of time-varying linearization and analysis of Perron effects of the Lyapunov exponent sign reversal, effective analytical-numerical method for the finite-time and exact Lyapunov dimension computation, and proof of the Eden conjecture for a number of dynamical systems.
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MATHEMATICS AND COMPUTERS IN SIMULATION (2024): 174-203
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICSno. 4 (2024): 3986-3995
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERSno. 12 (2023): 5408-5420
Materialsno. 18 (2023): 6099-6099
IFAC-PapersOnLineno. 2 (2023): 821-826
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IFAC-PapersOnLineno. 2 (2023): 4460-4465
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CHEMOSENSORSno. 1 (2023)
Materialsno. 18 (2023): 6133-6133
Chaos, Solitons & Fractals (2023): 113101-113101
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