论文标题
与rank-1鞍座的定期驱动系统的正常双曲线不变流形上的动力和分叉
Dynamics and bifurcations on the normally hyperbolic invariant manifold of a periodically driven system with rank-1 saddle
论文作者
论文摘要
在化学反应中，轨迹通常从反应物转向产物，当越过靠近正常双曲线不变的歧管（NHIM）的分裂表面，这是由稳定且不稳定的歧管的相交给出的。轨迹从原则上完全始于NHIM，当及时传播时，切勿离开这种歧管。当NHIM本身变得依赖时间时，这仍然适用于驱动系统。我们通过数值稳定运动来研究具有两个自由度的定期驱动模型系统的NHIM上的动力学。我们使用poincaré表面，证明了动力学的结构变化的发生，\ emph {viz。}，改变外部驾驶的幅度和频率时，周期性过渡状态（TS）轨迹的分叉。特别是，与普通的TS轨迹相比，与外部驱动相同但显着不同的参数具有相同时期的周期性TS轨迹，可以在鞍形节点分叉中创建。
In chemical reactions, trajectories typically turn from reactants to products when crossing a dividing surface close to the normally hyperbolic invariant manifold (NHIM) given by the intersection of the stable and unstable manifolds of a rank-1 saddle. Trajectories started exactly on the NHIM in principle never leave this manifold when propagated forward or backward in time. This still holds for driven systems when the NHIM itself becomes time dependent. We investigate the dynamics on the NHIM for a periodically driven model system with two degrees of freedom by numerically stabilizing the motion. Using Poincaré surfaces of section we demonstrate the occurrence of structural changes of the dynamics, \emph{viz.}, bifurcations of periodic transition state (TS) trajectories when changing the amplitude and frequency of the external driving. In particular, periodic TS trajectories with the same period as the external driving but significantly different parameters---such as mean energy---compared to the ordinary TS trajectory can be created in a saddle-node bifurcation.
