Research output: Contribution to journal › Article › peer-review
Decaying Oscillatory Perturbations of Hamiltonian Systems in the Plane. / Sultanov, O. A.
In: Journal of Mathematical Sciences (United States), Vol. 257, No. 5, 01.09.2021, p. 705-719.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Decaying Oscillatory Perturbations of Hamiltonian Systems in the Plane
AU - Sultanov, O. A.
PY - 2021/9/1
Y1 - 2021/9/1
N2 - We study the influence of decaying perturbations on autonomous oscillatory systems in a plane under the assumption that the perturbations preserve the equilibrium state of the limit system, oscillate with asymptotically constant frequency, and satisfy the nonresonance condition. We discuss the long-term behavior of the perturbed trajectories in a neighborhood of the equilibrium state. We describe conditions on the perturbation parameters that guarantee preservation or loss of stability of the equilibrium. The results are illustrated by an example of decaying perturbations of the Duffing oscillator.
AB - We study the influence of decaying perturbations on autonomous oscillatory systems in a plane under the assumption that the perturbations preserve the equilibrium state of the limit system, oscillate with asymptotically constant frequency, and satisfy the nonresonance condition. We discuss the long-term behavior of the perturbed trajectories in a neighborhood of the equilibrium state. We describe conditions on the perturbation parameters that guarantee preservation or loss of stability of the equilibrium. The results are illustrated by an example of decaying perturbations of the Duffing oscillator.
UR - http://www.scopus.com/inward/record.url?scp=85113887570&partnerID=8YFLogxK
U2 - 10.1007/s10958-021-05511-2
DO - 10.1007/s10958-021-05511-2
M3 - Article
AN - SCOPUS:85113887570
VL - 257
SP - 705
EP - 719
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
IS - 5
ER -
ID: 126272610