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Dynamical phenomena connected with stability loss of equilibria and periodic trajectories
journal contributionposted on 2022-02-09, 14:33 authored by Anatoly NeishtadtAnatoly Neishtadt, Dmitry Treschev
This 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.
Russian Science Foundation under grant no. 20-11-20141
- Mathematical Sciences
Published inRussian Mathematical Surveys
Pages883 - 926
- SMUR (Submitted Manuscript Under Review)
Rights holder© Russian Academy of Sciences (DoM), London Mathematical Society, IOP Publishing Limited
Publisher statementThis 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.
DepositorProf Anatoly Neishtadt. Deposit date: 22 September 2021
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