Dynamical phenomena connected with stability loss of equilibria and periodic trajectories
journal contributionposted on 09.02.2022, 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