The birth of the global stability theory and the theory of hidden oscillations

The first mathematical problems of the global analysis of dynamical models can be traced back to the engineering problem of the Watt governor design. Engineering requirements and corresponding mathematical problems led to the fundamental discoveries in the global stability theory. Boundaries of glob...

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Bibliographic Details
Published in:arXiv.org 2021-07
Main Authors: Kuznetsov, N V, Lobachev, M Y, Yuldashev, M V, Yuldashev, R V, Kudryashova, E V, Kuznetsova, O A, Rosenwasser, E N, Abramovich, S M
Format: Article
Language:English
Subjects:
Dynamic models
Mathematical problems
Oscillations
Stability criteria
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Summary:The first mathematical problems of the global analysis of dynamical models can be traced back to the engineering problem of the Watt governor design. Engineering requirements and corresponding mathematical problems led to the fundamental discoveries in the global stability theory. Boundaries of global stability in the space of parameters are limited by the birth of oscillations. The excitation of oscillations from unstable equilibria can be easily analysed, while the revealing of oscillations not connected with equilibria is a chalfilenging task being studied in the theory of hidden oscillations. In this survey, a brief history of the first global stability criteria development and corresponding counterexamples with hidden oscillations are discussed.
ISSN:2331-8422
DOI:10.48550/arxiv.2107.13889