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Dynamical phenomena connected with stability loss of equilibria and periodic trajectories

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journal contribution
posted on 09.02.2022, 14:33 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.

Funding

Russian Science Foundation under grant no. 20-11-20141

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Russian Mathematical Surveys

Volume

76

Issue

5

Pages

883 - 926

Publisher

Turpion

Version

SMUR (Submitted Manuscript Under Review)

Rights holder

© Russian Academy of Sciences (DoM), London Mathematical Society, IOP Publishing Limited

Publisher 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

16/08/2021

Publication date

2021-10-01

Copyright date

2021

ISSN

0036-0279

eISSN

1468-4829

Language

en

Depositor

Prof Anatoly Neishtadt. Deposit date: 22 September 2021