论文标题
振动性扰动下渐近自主的哈密顿系统的分叉
Bifurcations in asymptotically autonomous Hamiltonian systems under oscillatory perturbations
论文作者
论文摘要
研究了腐烂的振动扰动对具有稳定平衡的平面自主哈密顿系统的影响。假定扰动可以保持平衡并满足共振条件。研究了平衡附近的扰动轨迹的行为。根据扰动的结构，可能会及时地在无穷大的各种渐近方案。特别是，系统中可能发生相位锁定和相位漂移。该论文研究了与两种政权中平衡的稳定性变化有关的分叉。提出的稳定性分析基于平均方法和Lyapunov函数的构建的组合。
The effect of decaying oscillatory perturbations on autonomous Hamiltonian systems in the plane with a stable equilibrium is investigated. It is assumed that perturbations preserve the equilibrium and satisfy a resonance condition. The behaviour of the perturbed trajectories in the vicinity of the equilibrium is investigated. Depending on the structure of the perturbations, various asymptotic regimes at infinity in time are possible. In particular, a phase locking and a phase drifting can occur in the systems. The paper investigates the bifurcations associated with a change of Lyapunov stability of the equilibrium in both regimes. The proposed stability analysis is based on a combination of the averaging method and the construction of Lyapunov functions.
