Specific Poincaré map for a randomly-perturbed nonlinear oscillator
Specific Poincaré map for a randomly-perturbed nonlinear oscillator
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DOI：
10.1088/0305-4470/39/3/003
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发表时间：
2006-01
期刊：
影响因子：
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通讯作者：
D. Makarov;M. Uleysky
中科院分区：
文献类型：
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作者：
D. Makarov;M. Uleysky
用决定论方法研究了受弱随机力驱动的经典哈密顿振子的运动。我们设计了特定的Poincaré映射来寻找相空间中有限时间稳定的区域。根据Lyapunov准则，属于这些区域的轨迹至少在映射T0期间保持稳定。我们推导出了闭合轨迹之间的相位关联时间的下界。研究发现，某些稳定磁区的寿命明显超过外力的关联时间。以随机驱动的莫尔斯振荡器为例。
The motion of a classical Hamiltonian oscillator, driven by a weak random force, is examined by means of a deterministic approach. We design the specific Poincaré map to find domains of finite-time stability in phase space. The trajectories belonging to these domains remain stable by Lyapunov criteria for the period of mapping T0 at least. We derive the lower border for the time of phase correlations between close trajectories. It is found that the lifetime of some stable domains significantly exceeds the correlation time of the external force. The randomly-driven Morse oscillator is used as an example.