论文标题
具有乘法噪声的渐近自主哈密顿系统的长期行为
Long-term behaviour of asymptotically autonomous Hamiltonian systems with multiplicative noise
论文作者
论文摘要
研究了乘法随机扰动对平面上渐近汉密尔顿系统类别的影响。假定干扰不能保留相应限制系统的平衡及其强度在幂律渐进性中及时衰减。本文讨论了解决方案的长期渐近行为及其对扰动的结构和参数的依赖性。特别是，表明扰动的轨迹可能趋向于限制系统的均衡，或者可能出现新的随机稳定状态。提出的分析基于平均方法的组合和随机Lyapunov函数的构建。在存在噪声的情况下，获得的结果应用于捕获问题中的参数自动增生。
The influence of multiplicative stochastic perturbations on the class of asymptotically Hamiltonian systems on the plane is investigated. It is assumed that disturbances do not preserve the equilibrium of the corresponding limiting system and their intensity decays in time with power-law asymptotics. The paper discusses the long-term asymptotic behaviour of solutions and its dependence on the structure and parameters of perturbations. In particular, it is shown that perturbed trajectories can tend to the equilibrium of the limiting system or new stochastically stable states can arise. The proposed analysis is based on a combination of the averaging method and the construction of stochastic Lyapunov functions. The results obtained are applied to the problem of capture into parametric autoresonance in the presence of noise.
