Nikolay V. Kuznetsov

 

Address: Faculty of Mathematics and Mechanics, Saint-Petersburg State University, 28 Universitesky pr., Peterhof, Saint-Petersburg 198504, Russia

Phone: +7 (812) 4284015   Fax: +7 (812) 4286998

kuznetsov<at>math.spbu.ru  nkuznetsov239<at>gmail.com

Ph.D., Associated Professor

Applied Cybernetics Department,

Faculty of Mathematics and Mechanics,

Saint-Petersburg State University

2005 – now

Associated Professor of Saint-Petersburg State University, Faculty of Mathematics and Mechanics

 

2008

 

Ph.D. degree, University of Jyväskylä, Finland

2006

Specialist degree in Management (diploma with honors)

2004

Postdoctoral position in Max Plank Institute, Physics of Complex Systems, Dresden, Germany

Candidate of Sciences degree in Discrete mathematics and mathematical cybernetics, Saint-Petersburg State University

2001 –2004

Lecturer and Researcher: Faculties Management and Math. & Mech.; Research Institute of Math. & Mech.

2001

Specialist degree in Applied mathematics and informatics (diploma with honors), Saint-Petersburg State University, Faculty of Mathematics and Mechanics

 

INTERESTS

·       Dynamical systems

·       Phase synchronization and control

·       Computers and programming

·        IT-management

·        Nonlinear analysis of phase-locked loops (PLL)

[PDF slides]

·        Hidden oscillations and hidden attractor (describing function, Aizerman problem and Kalman problem on absolute stability, Chua circuits)

[PDF slides]

·        Lyapunov quantities and limit cycles (16th Hilbert problem)

[PDF slides]

·        Perron effects of Lyapunov exponent sign inversions and chaos (linearization, stability and instability by the first approximation)

[PDF slides]

 

PUBLICATIONS: author and co-author of more than 100 publications

Main publications

Monographs, book chapters and tutorials

·        V.O. Bragin, V.I. Vagaitsev, N.V. Kuznetsov, G.A. Leonov, Algorithms for Finding Hidden Oscillations in Nonlinear Systems. The Aizerman and Kalman Conjectures and Chua's Circuits, Journal of Computer and Systems Sciences International, 2011, Vol. 50, No. 4, pp. 511-543 [PDF] [DOI]

·        G.A. Leonov, N.V. Kuznetsov, O.A. Kuznetsova, S.M. Seledzhi, V.I.Vagaitsev, Hidden oscillations in dynamical systems, Transaction on Systems and Control, Issue 2, Volume 6, 2011, pp 54-67 [PDF]

·        N.V. Kuznetsov, G.A. Leonov, Lyapunov Quantities and Limit Cycles of Two-dimensional Dynamical Systems, (book chapter in "Dynamics and Control of Hybrid Mechanical Systems", editors G. Leonov, H. Nijmeijer, A. Pogromsky, A. Fradkov), World Scientific, 2010, pp. 7-28 [WEB]

·        G.A. Leonov, N.V. Kuznetsov, S.M. Seledzhi, Nonlinear Analysis and Design of Phase-Locked Loops, (book chapter in "Automation control – Theory and Practice", A.D. Rodić (Ed.), In-Tech, 2009), pp. 89-114 [PDF]

·        Kuznetsov N.V., Stability and Oscillations of Dynamical Systems: Theory and Applications. Jyväskylä University Printing House, 2008 [PDF]

·        G.A. Leonov, N.V. Kuznetsov, Time-Varying Linearization and the Perron effects, International Journal of Bifurcation and Chaos, Vol. 17, No. 4, 2007, pp. 1079-1107 [PDF] [DOI]

Journal and conference papers

·        Leonov G.A., Kuznetsov N.V., Vagaitsev V.I, Localization of hidden Chua's attractors, Physics Letters A, Vol. 375, is. 23, 2011, pp. 2230-2233 [PDF] [DOI]

·        G.A. Leonov, N.V. Kuznetsov, M.V. Yuldashev, R.V. Yuldashev, Computation of Phase Detector Characteristics in Synchronization Systems, Doklady Mathematics, 2011, Vol. 84, No. 1, pp. 586-590 [PDF] [DOI]

·        N.V. Kuznetsov, G.A. Leonov, M.V. Yuldashev, R.V. Yuldashev, Analytical methods for computation of phase-detector characteristics and PLL design, ISSCS 2011 – IEEE International Symposium on Signals, Circuits and Systems, Proceedings, 2011, Art. num. 5978639, pp.7-10 [DOI]

·        Kuznetsov N.V., Kuznetsovà O.A., Leonov G.A., Vagaitsev V.I., Hidden attractor in Chua's circuits, Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics, Volume 1, 2011, pp. 279-282 [DOI]

·        G.A. Leonov, N.V. Kuznetsov, Algorithms for Searching for Hidden Oscillations in the Aizerman and Kalman Problems, Doklady Mathematics, 2011, Vol. 84, No. 1, pp. 475-481 [PDF] [DOI]

·        G.A. Leonov, N.V. Kuznetsov, and E.V. Kudryashova, A Direct Method for Calculating Lyapunov Quantities of Two-Dimensional Dynamical Systems, Proceedings of the Steklov Institute of Mathematics, Volume 272, Supplement 1, 2011, pp. S119-S127 [PDF] [DOI]

·        Leonov G.A., Kuznetsov N.V., Seledzhi S.M., Shumafov M.M., Stabilization of unstable control system via design of delayed feedback, International Conference on Applied and Computational Mathematics, 2011, pp.18-25 [PDF]

·        G.A. Leonov, V.O. Bragin, N.V. Kuznetsov, Algorithm for Constructing Counterexamples to the Kalman Problem, Doklady Mathematics, 2010, Vol. 82, No. 1 pp. 540-542 [PDF] [DOI]

·        G.A. Leonov, V.I. Vagaitsev, N.V. Kuznetsov, Algorithm for localizing Chua attractors based on the harmonic linearization method, Doklady Mathematics, 2010, Vol. 82, No. 1, pp. 663-666 [PDF] [DOI]

·        G.A. Leonov, N.V. Kuznetsov, Limit Cycles of Quadratic Systems with a Perturbed Weak Focus of Order 3 and a Saddle Equilibrium at Infinity, Doklady Mathematics, 2010, Vol. 82, No. 2, 693-696 [PDF] [DOI]

·        G.A. Leonov, N.V. Kuznetsov, S.M. Seledzhi, K.E. Starkov, Localization of the Attractor of the Differential Equations for the Solar Wind-Magnetosphere-Ionosphere Model, Doklady Physics, 2010, Vol. 55, No. 9, pp. 471-473 [PDF] [DOI]

·        G.A. Leonov, N.V. Kuznetsov, and E.V. Kudryashova, Cycles of Two-Dimensional Systems: Computer Calculations, Proofs, and Experiments, Vestnik St. Petersburg University. Mathematics, Vol. 41, No. 3, pp. 216-250, 2008 (Allerton Press, USA) [DOI]

·        Kuznetsov N.V., Leonov G.A., Lyapunov quantities, limit cycles and strange behavior of trajectories in two-dimensional quadratic systems, Journal of Vibroengineering, Vol. 10, Iss. 4, 2008, pp. 460–467 [PDF]

·        N.V. Kuznetsov, V. Reitmann, Realization theory methods for the construction of positively-invariant sets, Proceedings of the 3rd International IEEE Scientific Conference on Physics and Control, 2007 [PDF]

·        Leonov G.A., Kuznetsov N.V., Computation of the first Lyapunov quantity for the second-order dynamical system, IFAC Proceedings Volumes (IFAC-PapersOnline), Vol. 3, Issue 1, 2007, pp. 87-89 [DOI]

·        N.V. Kuznetsov, G.A. Leonov, H. Nijmeijer, A. Pogromsky, Synchronization of two metronomes, IFAC Proceedings Volumes (IFAC-PapersOnline), Vol. 3, Issue 1, 2007, pp. 49-52 [PDF] [DOI]

·        Kuznetsov N.V., Leonov G.A., Criteria of stability by the first approximation for discrete nonlinear systems, Vestnik St. Petersburg University. Mathematics. Vol. 38, No. 3, pp. 21-30, 2005 (Allerton Press, USA) [WEB]

·        Kuznetsov N.V., Leonov G.A., Criterion of stability to first approximation of nonlinear discrete systems, Vestnik St. Petersburg University. Mathematics. Vol. 38, No. 2, pp. 52-60, 2005 (Allerton Press, USA) [WEB]

·        N. Kouznetsov, V. Reitmann, H. Kantz, Imbedding of causal time-series into a universal nonlinear scattering model of Boltzmann-type, Report of 3rd annual meeting of the DFG-Schwerpunktprogramm 1114, Universitat Bremen, 2004, pp. 1-21 [PDF]

·        Kuznetsov N.V., Stability of one class of differential-functional equations in the most simple critical case of monotone differentiable nonlinear characteristic, Differential Equations And Control Processes, ¹3, 2003, pp. 56–65 [WEB]

·        N.V. Kuznetsov, On the stability of nonlinear systems with the monotonic differentiable nonlinear characteristics, Differential Equations And Control Processes, ¹1, pp. 11-16, 2001 [PDF]

·        Gelig A.K., Kuznetsov N.V., Oscillations in pulse-width modulated system, 2nd International conference "Control of Oscillations and Chaos", 2000, Proceedings. Volume 2, pp. 294-295 [DOI]

Keynote and invited lectures

·        Kuznetsov N.V., Hidden oscillations and hidden attractor in dynamical systems, Annual Computational Science Day 2011 (Lappeenranta, Finland) (survey lecture) [PDF]

·        Leonov G.A., Kuznetsov N.V., Analytical-numerical methods for investigation of hidden oscillations in nonlinear control systems, 18th World Congress of the International Federation of Automatic Control, 2011 (Milan, Italy) (survey paper) [DOI]

·        G. Leonov, N. Kuznetsov, Modern problems in applied dynamical systems theory (Stability, Hidden oscillation and hidden attractor localization, Strange attractors, dimension, and Lyapunov exponents, Dynamical models: Electrical machines and phase locked loops), 21st Jyväskylä Summer School, 2011 (Jyväskylä, Finland) (invited lecture)

·        Leonov G.A., Kuznetsov N.V., Seledzhi S.M., Analytical-numerical methods for hidden oscillations localization, ECCOMAS Thematic Conference Computational Analysis and Optimization, 2011 (Jyväskylä, Finland) (keynote lecture)

·        Leonov G.A., Kuznetsov N.V., Kuznetsova O.A., Zarezkiy A.M., Seledzhi S.M., Solov'eva E.P., Vagaitsev V.I., Yuldashev M.V., Yuldashev R.V., Invention of new methods of synchronizing, International Conference TRIZfest-2011, 2011 (St.Petersburg, Russia) (plenary lecture)

·        G.A. Leonov, N.V. Kuznetsov, E.V. Kudryashova, Local methods for dynamic system cycle investigation, X International Workshop "Stability and Oscillations of Nonlinear Control Systems", 2008 (Moscow, Russia) (plenary lecture)

Patents

·        Method for determining the operating parameters of phase-locked oscillator and device for its implementation, ¹2010149471, 2011

·        Tool for modeling the phase detector parameters, ¹2011113212, 2011

 

PhD THESIS SUPERVISION

·        Vitaly Bragin (St. Petersburg State Univ., 2010)

·        Elena V. Kudryashova (Ph.D

, Univ. of Jyväskylä, St. Petersburg State Univ., 2009)

 

EDITORIAL BOARDS and EDITORS

·        International Journal of Bifurcation and Chaos

·        Journal of Applied Nonlinear Dynamics

·        Journal of Differential Equations and Control Processes

 

FELLOWSHIPS

·        Eindhoven University of Technology, The Netherlands (2006, 2008)

·        Max Plank Institute, Physics of Complex Systems, Dresden, Germany (2004)

·        Frie University of Berlin, Germany (2002), DAAD fellowship program

·        University of Heidelberg, Germany (2000), DAAD fellowship program

 

AWARDS, PERSONAL GRANTS

·        Paper award at 8th Int. Conference on Informatics in Control, Automation and Robotics («Hidden attractor in Chua's circuits», 2011)

·        Grant from Academy of Finland for postdoc (2011-2013)

·        Contracts from Ministry of Education and Science of the Russian Federation (Federal target program, 2009-2013)

·        Scholarship from Jyväskylä Graduate School in Computing and Mathematical Sciences (2008)

·        Paper award at Int. Conference Space, astronomy and programming (2008)

·        Scholarships from the Government of Saint-Petersburg for postdoc (2007, 2008, 2010, 2011)

·        Grant form Grants board of The President of the Russian Federation for postdoc (2007-2008)

·        Grant for PhD students from Russian Ministry of Common and Professional Education (2003-2004)

·        Scholarship from the Government of Russian Federation (2003)

·        Scholarships from the Government of Saint-Petersburg for postgraduate students (2002, 2003, 2004)

·        Winner of DAAD Leonhard-Euler-Programm (2000, 2002)

 

PARTICIPATION IN INTERNATIONAL SCINTIFIC PROJECTS

·        The interdisciplinary center of excellence, German-Russian Interdisciplinary Science Center (G-RISC) in Saint-Petersburg State University, 2009-2013 (leader: Prof. E. Ruehl, Germany)

·        CONACYT project "Localization Analysis of Compact Invariant Sets of Systems with Complex Dynamics and its Applications" ¹000000000078890, 2007-2010 (leader: Prof. K. Starkov, Mexico)

·        NWO–RFBR Dutch-Russian cooperation program "Dynamics and control of hybrid mechanical systems" ¹047.011.2004.004, 2005–2008 (leaders: Prof. H. Nijmeijer, The Netherlands, Prof. G.A. Leonov, Russia)

·        DFG Schwerpunktprogramme 1114 – German Priority Research Program "Mathematical methods for time series analysis and digital image processing", 2002-2006 (leader: Prof. Dr. H. Kantz, Germany)

 

CONFERENCES ORGANIZATION

·        4th IFAC Workshop on Periodic Control System, 2010

·        6th EUROMECH Nonlinear Dynamics Conference, 2008

·        International congress Nonlinear Dynamical Analysis, 2007

·        3rd IFAC Workshop on Periodic Control System, 2007

·        2nd International conference Control of Oscillations and Chaos, 2000