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, 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.

在化学反应中，当通过靠近第1级鞍座的稳定歧管和不稳定歧管的交点的，通常为双曲不变歧管（NHIM）的分隔表面时，轨迹通常从反应物转变为产物。轨迹恰好在NHIM上开始，原则上在时间向前或向后传播时永远不会离开该流形。当NHIM本身随时间变化时，这对于驱动系统仍然适用。我们通过数值稳定运动来研究具有两个自由度的周期性驱动模型系统的NHIM动力学。使用截面的庞加莱曲面，我们演示了动力学结构变化的发生，即。当改变外部驱动的幅度和频率时，周期性过渡状态（TS）轨迹的分叉。特别是，可以在鞍形节点分叉中创建与外部驱动相同周期但与普通TS轨迹相比参数（例如平均能量）明显不同的周期性TS轨迹。