The needle in the haystack – is it there and can I find it? (Mokaev)
The oscillations of dynamical systems have been studied for more than a century and several theoretical methods have been presented. However, none of the methods is powerful enough to give a complete solution to the problem. Rather the contrary, in the last years more and more examples have been found of so called hidden oscillations – oscillatory modes of systems that are hard to predict and detect by any systematic method but yet as harmful as any uncontrolled oscillation in a system that is expected to be stable.
MSc Ruslan Mokaev’s dissertation presents a systematic comparison of several classical methods for analyzing the stability of systems and applies this comparison to a model of an airplane flutter control mechanism. It turns out that none of the methods is strictly superior to its competitors and that every method ignores some hidden oscillatory regimes.
According to the research, this calls for further study about the stability of systems and about the limitations of the current design methods. To this end, the dissertation provides, for the first time, a characterization of a family of systems that are guaranteed to have hidden oscillations. This characterization helps to define test cases for the analysis and visualization algorithms used in the study of chaotic oscillations.
MSc Ruslan Mokaev defends his doctoral dissertation in Mathematical Information Technology "Effective analytical-numerical methods for study of regular and chaotic oscillations in dynamical systems" on December 14th 2019. The doctoral dissertation takes place in Ä¢¹½Ö±²¥, Agora-building, hall Gamma, and starts at 12 pm. Opponent is Professor Vladimir Răsvan (University of Craiova, Romania) and Custos Professor Nikolay Kuznetsov (Ä¢¹½Ö±²¥). The doctoral dissertation is held in English.
Further information:
Ruslan Mokaev, mokaev.ruslan@gmail.com
MSc Ruslan Mokaev graduated from the Presidential Physics and Mathematics Lyceum â„– 239, St. Petersburg in 2008. He received his MSc in 2013 from the Saint-Petersburg State University. Since his graduation, Mokaev has worked as a Junior Researcher at the Faculty of Mathematics and Mechanics of Saint-Petersburg State University.
The dissertation is published in the series JYU Dissertations, number 172, 84 p. (+included articles), Jyväskylä: Ä¢¹½Ö±²¥, 2019, ISSN 2489-9003, ISBN 978-951-39-7989-8 (PDF). Link to the publication: