Nikolay V. Kuznetsov

{{Infobox scientist

| name = Nikolay V. Kuznetsov

|image =

|birth_date = {{birth date and age|1979|5|13|df=y}}

|birth_place = Leningrad

|death_date =

|death_place =

|fields = nonlinear dynamics, control

|workplaces = St. Petersburg University, University of Jyväskylä

|alma_mater = St. Petersburg University

|academic_advisors =

|known_for = theory of hidden oscillations, hidden attractors, nonlinear analysis of phase-locked loops

|awards = National Awards of the Russian Federation in Science and Technology (2025), Andronov Prize (2024), Afraimovich Award (2021), Highly Cited Researchers (2019-2021), Medal of the University of Jyväskylä (2017)

| doctoral_students = [https://genealogy.math.ndsu.nodak.edu/id.php?id=131379&fChrono=1 see Mathematics Genealogy Project]

}}

Nikolay Vladimirovich Kuznetsov ({{langx|ru|Николай Владимирович Кузнецов}}; born 13 May 1979 in Leningrad, USSR) is a specialist in nonlinear dynamics and control theory, and the founder of the theory of hidden oscillations.

Academic career

He graduated from the St. Petersburg University, Department of Theoretical Cybernetics chaired by V.A. Yakubovich, in 2001. In 2004 he received Candidate of Science degree (supervisor G.A. Leonov) and in 2016 Doctor of Science degree (Habilitation) from St. Petersburg University. From 2003 Nikolay Kuznetsov has been working in St. Petersburg University and now he is Full professor (tenured) and Head of the Department of Applied Cybernetics there. Since 2018 the research group chaired by Kuznetsov has been awarded the status of the Leading Scientific School (Center of Excellence) of Russia in the field of mathematics and mechanics. In 2020 he was named Professor of the Year in the field of mathematics and physics in Russia.

[[File:2017-JYU-Medal-KuznetsovNV.jpg|thumb|

Medal of the University of Jyväskylä is awarded to Prof. Kuznetsov (2017).]]

Since 2018, Kuznetsov is Head of the Laboratory of information and control systems at the Institute for Problems in Mechanical Engineering of the Russian Academy of Science. In 2022, Nikolay Kuznetsov was elected a member of the Russian Academy of Science.

In 2008, Kuznetsov defended his Ph.D. degree at the University of Jyväskylä, Finland (supervisors P. Neittaanmäki, G.A. Leonov).

After the defense, he has been working at the University of Jyväskylä as the Academy of Finland postdoc,

then as a part-time professor at the IT Faculty: from 2014 he is Adjunct Docent and from 2017 – Visiting Professor.

He is co-chair of the Finnish-Russian educational & research program organized in 2007

by the University of Jyväskylä and St. Petersburg University.[https://www.youtube.com/watch?v=zYRj7gc0ULE Ph.D. defense at the University of Jyväskylä in the framework of the Finnish-Russian educational & research PhD program (Custos Prof. N. Kuznetsov, 14.12.2019)] As a recognition, University of Jyväskylä awarded him a medal for his distinguished merits in the field of applied mathematics and training doctoral students,[https://www.jyu.fi/en/news/archive/2017/12/tiedote-2017-12-18-14-50-34-744897 Medal of the University of Jyväskylä to IT Faculty Professor Nikolay Kuznetsov (2017)] in 2020 he got the Finnish Information Processing Association (TIVIA) award{{cite web|url= https://tivia.fi/2020/07/02/tivia-keski-suomi-ryn-vuoden-2019-tunnustuspalkinnot | title= TIVIA Keski-Suomi ry:n vuoden 2019 tunnustuspalkinnot

|publisher = TIVIA

|date = 2020-07-02}} and was elected a foreign member of the Finnish Academy of Science and Letters (becoming its youngest foreign member at the time of election).{{cite book |last=Aula|first=P.|date=2021 |title= Finnish Academy of Science and Letters. Year book 2020 | url=https://www.yumpu.com/fi/document/view/68386344/finnish-academy-of-science-and-letters-year-book-2022| isbn=978-951-41-1171-6}}[https://www.jyu.fi/en/current/archive/2020/09/four-top-scientists-from-the-university-of-jyvaskyla-chosen-as-new-members-of-the-finnish-academy-of-science-and-letters Four top scientists from the University of Jyväskylä chosen as new members of the Finnish Academy of Science and Letters, 14.09.2020][https://eurohighereducation.com/2020/09/27/four-top-scientists-from-the-university-of-jyvaskyla-chosen-as-new-members-of-the-finnish-academy-of-science-and-letters/ Four top scientists from the University of Jyväskylä chosen as new members of the Finnish Academy of Science and Letters. European Higher Education Organization. 27.09.2020] In 2021, the joint educational & research program was expanded to include the Lappeenranta-Lahti University of Technology, where Kuznetsov was offered the position of Visiting Professor. The experience of the program he used in 2013 when organizing the first

defenses to the Ph.D. degree granted by St. Petersburg University,

instead of the Candidate of Sciences degrees awarded by the State Supreme Certification Commission.[http://math.spbu.ru/user/nk/PDF/2013-First-PhD-SPbSU-Renat-Yuldashev-Supervisors.pdf N.V. Kuznetsov, P. Neittaanmäki, G.A. Leonov, Supervisors' manifest on the first Ph.D. SPbSU (2013)]

Scientific work

File:Afraimovich Award Diploma 2021.jpg Award granted to N. Kuznetsov for The theory of hidden oscillations and stability of dynamical systems (2021)]]

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. N. Kuznetsov introduced the concept of self-excited and hidden attractors, laying out the foundations for the theory of hidden oscillations.{{cite book |last=Alexeeva|first=T.|date=2024 |title= Forecasting and control in nonlinear economic models with application to economic policy |publisher=LUT University Press | url=https://lutpub.lut.fi/bitstream/handle/10024/168153/Tatiana%20Alekseeva_A4.pdf#page=40}}{{rp|39}} Among his main results are the discovery of a hidden Chua attractor in Chua circuits,{{cite web|url= https://www.worldscientific.com/na101/home/literatum/publisher/wspc/journals/content/ijbc/2017/ijbc.27.issue-12/ijbc.27.issue-12/20171218/ijbc.27.issue-12.cover.jpg |title= The Cover of the International Journal of Bifurcation and Chaos 27(12), 2017 with coexisting hidden Chua attractor. Article Scenario of the birth of hidden attractors in the Chua circuit by N.V. Stankevich, N.V. Kuznetsov, G.A. Leonov, L. Chua}} revealing of coexisting hidden attractors in electromechanical models with Sommerfeld effect, solutions to the Egan problem on the pull-in range, to the Gardner problem on the lock-in range, and to the Viterbi problem on the coincidence of phase-locked loop ranges 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.

The Web of Science Group proclaimed Kuznetsov a Highly Cited Researcher in Russia twice over two consecutive years (2016-2017) and included him in the worldwide list of Highly Cited Researchers in 2019[https://recognition.webofsciencegroup.com/awards/highly-cited/2019/ Highly Cited Researchers 2019 (Web of Science)]

(where he was among 3 scientists from St. Petersburg University and the only one from the University of Jyväskylä),[https://www.jyu.fi/fi/ajankohtaista/arkisto/2019/11/jyvaskylan-yliopiston-professori-vuoden-viitatuimpien-joukossa Professor at the University of Jyväskylä, one of the year's most cited (27.11.2019)]{{cite web

| url = https://www.sttinfo.fi/tiedote/jyvaskylan-yliopiston-professori-vuoden-viitatuimpien-joukossa?publisherId=69817172&releaseId=69870292

| title = Jyväskylän yliopiston professori vuoden viitatuimpien joukossa

| publisher = «Finnish News Agency»

| accessdate = 2019-11-27

}} 2020,[https://www.jyu.fi/en/current/archive/2020/11/jyu-in-the-highly-cited-researchers-list-2020 JYU in the Highly Cited Researchers list 2020 (30.11.2019)]{{cite web

| url = https://agenparl.eu/among-the-six-russian-scientists-included-in-the-top-most-cited-scientists-in-the-world-there-are-three-researchers-from-st-petersburg-university/

| title = Among the six Russian scientists included in the top most cited scientists in the world, there are three researchers from St Petersburg University

| publisher = «Agenparl - L'informazione indipendente»

| accessdate = 2020-12-17

}} and 2021.[https://www.jyu.fi/en/current/archive/2021/11/two-jyu-professors-in-the-world-list-of-super-researchers Two JYU professors in the world list of super researchers (23.11.2021)]

He was awarded the St. Petersburg University Prize in 2020, the Afraimovich Award of NSC society in 2021, and the Andronov Prize of the Russian Academy of Science in 2024 for the theory of hidden oscillations and stability of dynamical systems.{{cite web|url=https://ipme.ru/en/news/134-pozdravljaem-n-v-kuznecova-s-prisuzhdeniem-premii-ran-imeni-akademika-a-a-andronova.html| website=Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences| lang=en| title=Congratulations to Nikolay V. Kuznetsov on being awarded the Andronov Prize by the Russian Academy of Science|year=2024| access-date=28 July 2024}} In 2025, Nikolay V. Kuznetsov was awarded National Awards of the Russian Federation in Science and Technology (the highest scientific award of the Russian Federation) for creating and developing a new scientific field - the theory of hidden oscillations.{{cite web|url=http://en.kremlin.ru/supplement/6342|title=Laureates of the 2024 National Awards of the Russian Federation in Science and Technology|lang=en|publisher=kremlin.ru|date=2025-06-10|accessdate=2025-06-10}}

Additional information

[https://scholar.google.ru/citations?user=EjseyeQAAAAJ N.V. Kuznetsov at Google scholar]
[https://www.scopus.com/authid/detail.uri?authorId=57218598820 N.V. Kuznetsov at Scopus]
[https://www.webofscience.com/wos/author/record/F-4948-2011 N.V. Kuznetsov at Web of Science]
[https://genealogy.math.ndsu.nodak.edu/id.php?id=131379&fChrono=1 N.V. Kuznetsov at Mathematics Genealogy Project]
[https://research.com/scientists-rankings/mathematics/ru World Top Mathematics Scientists]
[https://english.spbu.ru/news-events/news/mathematician-nikolay-kuznetsov-st-petersburg-university-challenge-we-are-going Mathematician Nikolay Kuznetsov at St. Petersburg University. St. Petersburg University News. 10 Jan 2022]
[https://iopscience.iop.org/article/10.1088/1742-6596/1864/1/012066/pdf Abramovich S., Kuznetsov N., Razov A., G.A. Leonov: eminent scholar, admired teacher and unconventional administrator, Journal of Physics: Conference Series, Vol. 1864, 2021, art. num. 012066.]
[https://www.sciencedirect.com/science/article/pii/S2405896315012318 S. Abramovich, N. Kuznetsov, G. Leonov. V. A. Yakubovich — mathematician, “father of the field”, and herald of intellectual democracy in science and society, IFAC-PapersOnLine, 48(11), 2015, 1–3] ([https://www.youtube.com/watch?v=atO1PewvzGQ video])

Selected lectures

[https://www.youtube.com/watch?v=-CzGtbfi8g0 N.Kuznetsov, Keynote lecture Hidden attractors in science and technologies, General meeting of the Finnish Academy of Science and Letters, Finland, 2021]
[https://www.youtube.com/watch?v=l1hI2U-Bl28 N.Kuznetsov, Invited lecture The theory of hidden oscillations and stability of dynamical systems, Int. Workshop on Applied Mathematics, Czech Republic, 2021]
[https://www.youtube.com/watch?v=WbfXz4iBN0I N. Kuznetsov, Afraimovich award plenary lecture The theory of hidden oscillations and stability of dynamical systems, Int. Conference on Nonlinear Dynamics and Complexity, USA, 2021]

Selected publications: books and surveys

{{cite journal

| title=The Gardner Problem on the Lock-In Range of Second-Order Type 2 Phase-Locked Loops | journal= IEEE Transactions on Automatic Control

| volume= 68| pages=7436–7450| doi=10.1109/TAC.2023.3277896 | year=2023

| issue=12| doi-access=free}}

{{cite journal |author1=Kuznetsov N. V.|author2= Mokaev T. N. |author3=Ponomarenko V. I. |author4=Seleznev E. P. |author5= Stankevich N. V. |author6=Chua L. |year= 2023 |title= Hidden attractors in Chua circuit: mathematical theory meets physical experiments |journal= Nonlinear Dynamics |volume= 111|issue= 6|pages= 5859–5887|doi= 10.1007/s11071-022-08078-y| url=https://link.springer.com/content/pdf/10.1007/s11071-022-08078-y.pdf |bibcode= |s2cid= 255049732}}
{{cite book | first1= Nikolay | last1=Kuznetsov |

publisher = Springer| location = Cham| doi=10.1007/978-3-030-50987-3 | isbn=978-3-030-50986-6 | s2cid=224845580 |url=https://link.springer.com/content/pdf/10.1007/978-3-030-50987-3.pdf}}

{{cite book

publisher = Springer| location = Cham| doi=10.1007/978-3-030-75821-9 | isbn=978-3-030-75820-2 | s2cid=244816603 |url=https://link.springer.com/content/pdf/10.1007/978-3-030-75821-9.pdf}}

{{cite journal |

author1=Kuznetsov N.V. |

year = 2020|

title = Theory of hidden oscillations and stability of control systems|

journal = Journal of Computer and Systems Sciences International|

volume = 59| number = 5|pages = 647–668|

url = https://link.springer.com/content/pdf/10.1134/S1064230720050093.pdf|

doi = 10.1134/S1064230720050093|

s2cid = 225304463}}

{{cite journal

| title=Nonlinear Analysis of Charge-Pump Phase-Locked Loop: The Hold-In and Pull-In Ranges | journal= IEEE Transactions on Circuits and Systems I: Regular Papers

| volume= 68| pages=4049–4061| doi=10.1109/TCSI.2021.3101529 | year=2021

| issue=10| doi-access=free| arxiv=2005.00864}}

{{cite journal

| last1=Kuznetsov | first1=N.V.

| last2=Lobachev | first2=M.Y.

| last3=Yuldashev | first3=M.V.

| last4=Yuldashev | first4=R.V.

| title=The Egan problem on the pull-in range of type 2 PLLs

| journal=IEEE Transactions on Circuits and Systems II: Express Briefs

| doi=10.1109/TCSII.2020.3038075

| volume=68 | issue=4 | pages=1467–1471

| year=2021

| doi-access=free

}}

{{Cite journal |

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

doi=10.1007/s11071-020-05856-4|doi-access=free|url=https://link.springer.com/content/pdf/10.1007/s11071-020-05856-4.pdf}}

{{Cite journal

|first1=N.V. |last1=Kuznetsov

|first2=G.A. |last2=Leonov

|first3=T.N. |last3=Mokaev

|first4=A. |last4=Prasad

|first5=M.D. |last5=Shrimali

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

|journal=Nonlinear Dynamics

|url=https://link.springer.com/content/pdf/10.1007/s11071-018-4054-z.pdf?pdf=button}}

{{cite journal |

year = 2016 |

title = Hidden attractors in dynamical systems |

journal = Physics Reports |

volume = 637 | pages = 1–50|

doi =10.1016/j.physrep.2016.05.002|bibcode= 2016PhR...637....1D |url= https://jyx.jyu.fi/bitstream/handle/123456789/50751/1s2.0s0370157316300928main.pdf }}

{{cite journal

| last1=Best | first1=R.

| last2=Kuznetsov | first2=N.V.

| last3=Leonov | first3=G.A.

| last4=Yuldashev | first4=M.V.

| last5=Yuldashev | first5=R.V.

| title= Tutorial on dynamic analysis of the Costas loop

| journal= IFAC Annual Reviews in Control

| volume=42 | pages=27–49

| doi=10.1016/j.arcontrol.2016.08.003

| year=2016

| bibcode=

| s2cid=10703739

| url=https://zenodo.org/record/896255

| arxiv=1511.04435

}}

{{cite journal

| last1=Leonov | first1=G. A.

| last2=Kuznetsov | first2=N. V.

| last3=Yuldashev | first3=M. V.

| last4=Yuldashev | first4=R. V.

| title=Hold-in, pull-in, and lock-in ranges of PLL circuits: rigorous mathematical definitions and limitations of classical theory.

| journal=IEEE Transactions on Circuits and Systems I: Regular Papers

| publisher=IEEE

| volume=62 | issue=10 | pages=2454–2464

| doi=10.1109/TCSI.2015.2476295

|arxiv=1505.04262

| year=2015

| s2cid=12292968

}}

{{cite journal | last1=Leonov | first1=G. A.

| last2=Kuznetsov | first2=N. V.

|year= 2013 |title= Hidden attractors in dynamical systems. From hidden oscillations in Hilbert–Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits |journal= International Journal of Bifurcation and Chaos |volume= 23 |issue= 1 |pages= 1330002–219 |doi= 10.1142/S0218127413300024|bibcode=2013IJBC...2330002L |doi-access= free }}