February 7, 2019

Talk of Prof. Nikolay Kuznetsov

--- Title: Theory of Hidden Oscillations

February 7, 2019

Prof. Nikolay Kuznetsov
Applied Cybernetics Department
Saint Petersburg State University, Russia


Tuesday 2019-02-07 16:00
IST-Seminar-Room 2.255 - Pfaffenwaldring 9 - Campus Stuttgart-Vaihingen




In 2009, after the discovery in the Chua's circuit a hidden chaotic attractor, new classification of attractors as being hidden or self-excited was suggested. This was the beginning of development the theory of hidden oscillations which represents the genesis of the modern era of Andronov's theory of oscillations. An attractor is called self-excited if its basin of attraction intersects with any vicinity of an equilibrium, otherwise it is called a hidden attractor. Nowadays self-excited attractors can be easily revealed numerically by numerical integration of trajectories, started in small neighbourhoods of unstable equilibria. For a hidden attractor, its basin of attraction is not connected with equilibria, and, thus, the search and visualization of hidden attractors in the phase space may be a challenging task. The classification, not only demonstrated difficulties of fundamental problems (e.g., the second part of Hilbert's 16th problem on the number and mutual disposition of limit cycles, Aizerman's and Kalman's conjecture on the monostability of nonlinear systems) and applied systems analysis, but also triggered the discovery of new hidden attractors in well-known engineering and physical models.






Biographical Information



Nikolay  V.  Kuznetsov graduated from St. Petersburg State University. He received his Candidate of Science degree from St. Petersburg State University in 2004, Ph.D. degree from the University of Jyväskylä in 2008, Habilitation from St. Petersburg State University in 2016. From 2003 till now Nikolay Kuznetsov has been working in St. Petersburg State University. Now he is Professor, Head of the Department of Applied Cybernetics. In 2017 the research group headed by N. Kuznetsov was named among the Leading Scientific Schools of the Russian Federation and got special grant from the Russian President’s Grant Council (1 of 5 in mathematics and mechanics).

Kuznetsov is the coordinator of the Russian-Finnish Educational & Research program organized by St. Petersburg State University (Russia) and University of Jyväskylä (Finland). From 2017 – Visiting Professor at the University of Jyväskylä.

Kuznetsov is author and co-author of more than 200 articles and monographs (https://scholar.google.ru/citations?user=EjseyeQAAAAJ). His interests are now in dynamical systems stability and oscillations, nonlinear control systems, and phase-locked loop, differential inclusions, chaos, Lyapunov dimension of attractors.



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