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Dynamical phenomena connected with stability loss of equilibria and periodic trajectories
journal contribution
posted on 2022-02-09, 14:33 authored by Anatoly NeishtadtAnatoly Neishtadt, Dmitry TreschevThis is a study of a dynamical system depending on a parameter κ. Under the assumption that the system has a family of equilibrium positions or periodic trajectories smoothly depending on κ, the focus is on details of stability loss through various bifurcations (Poincaré–Andronov– Hopf, period-doubling, and so on). Two basic formulations of the problem are considered. In the first, κ is constant and the subject of the analysis is the phenomenon of a soft or hard loss of stability. In the second, κ varies slowly with time (the case of a dynamic bifurcation). In the simplest situation κ = εt, where ε is a small parameter. More generally, κ(t) may be a solution of a slow differential equation. In the case of a dynamic bifurcation the analysis is mainly focused around the phenomenon of stability loss delay.
Funding
Russian Science Foundation under grant no. 20-11-20141
History
School
- Science
Department
- Mathematical Sciences
Published in
Russian Mathematical SurveysVolume
76Issue
5Pages
883 - 926Publisher
TurpionVersion
- SMUR (Submitted Manuscript Under Review)
Rights holder
© Russian Academy of Sciences (DoM), London Mathematical Society, IOP Publishing LimitedPublisher statement
This paper was submitted for publication in the journal Russian Mathematical Surveys and the definitive published version is available at https://doi.org/10.1070/RM10023.Acceptance date
2021-08-16Publication date
2021-10-01Copyright date
2021ISSN
0036-0279eISSN
1468-4829Publisher version
Language
- en
Depositor
Prof Anatoly Neishtadt. Deposit date: 22 September 2021Usage metrics
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