Research output: Contribution to journal › Article › peer-review
Stability and bifurcation phenomena in asymptotically Hamiltonian systems. / Sultanov, Oskar A.
In: Nonlinearity, Vol. 35, No. 5, 05.05.2022, p. 2513-2534.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Stability and bifurcation phenomena in asymptotically Hamiltonian systems
AU - Sultanov, Oskar A.
PY - 2022/5/5
Y1 - 2022/5/5
N2 - The influence of time-dependent perturbations on an autonomous Hamiltonian system with an equilibrium of center type is considered. It is assumed that the perturbations decay at infinity in time and vanish at the equilibrium. In this case the stability and the long-term behaviour of trajectories depend on nonlinear and non-autonomous terms of equations. The paper investigates bifurcations associated with a change of Lyapunov stability of the equilibrium and the emergence of new attracting or repelling states in the perturbed non-autonomous system. The dependence of bifurcations on the structure of perturbations is discussed.
AB - The influence of time-dependent perturbations on an autonomous Hamiltonian system with an equilibrium of center type is considered. It is assumed that the perturbations decay at infinity in time and vanish at the equilibrium. In this case the stability and the long-term behaviour of trajectories depend on nonlinear and non-autonomous terms of equations. The paper investigates bifurcations associated with a change of Lyapunov stability of the equilibrium and the emergence of new attracting or repelling states in the perturbed non-autonomous system. The dependence of bifurcations on the structure of perturbations is discussed.
KW - 34C23
KW - 34D10
KW - 34D20
KW - 37J65
KW - asymptotics
KW - bifurcation
KW - Lyapunov function
KW - non-autonomous systems
KW - stability
UR - http://www.scopus.com/inward/record.url?scp=85129672657&partnerID=8YFLogxK
U2 - 10.1088/1361-6544/ac6372
DO - 10.1088/1361-6544/ac6372
M3 - Article
AN - SCOPUS:85129672657
VL - 35
SP - 2513
EP - 2534
JO - Nonlinearity
JF - Nonlinearity
SN - 0951-7715
IS - 5
ER -
ID: 126272295