论文标题
扩展过渡路径理论：定期驱动和有限的时间动态
Extending Transition Path Theory: Periodically-Driven and Finite-Time Dynamics
论文作者
论文摘要
给定两个不同的子集$ a，b $在某些动态系统的状态空间中，过渡路径理论（TPT）成功地用于描述固定系统的ergodic限制中从$ a $ a $ a $ a $ a $ a $ b $的统计行为。我们得出了tpt的概括，以消除平稳性和沿阵行的限制的要求，并为分析其他动态场景提供了这种强大的工具：定期强制强制动态和时间依赖时间的有限时间系统。这是通过研究气候，海洋和社会动态等应用的部分动机。在简单的模型示例中，我们展示了新工具如何能够对此类系统的统计行为提供定量理解。我们还指出了明确的情况，即更一般的动态制度对其固定式对应物显示出不同的行为，将这些工具直接链接到非确定性系统中的分叉。
Given two distinct subsets $A,B$ in the state space of some dynamical system, Transition Path Theory (TPT) was successfully used to describe the statistical behavior of transitions from $A$ to $B$ in the ergodic limit of the stationary system. We derive generalizations of TPT that remove the requirements of stationarity and of the ergodic limit, and provide this powerful tool for the analysis of other dynamical scenarios: periodically forced dynamics and time-dependent finite-time systems. This is partially motivated by studying applications such as climate, ocean, and social dynamics. On simple model examples we show how the new tools are able to deliver quantitative understanding about the statistical behavior of such systems. We also point out explicit cases where the more general dynamical regimes show different behaviors to their stationary counterparts, linking these tools directly to bifurcations in non-deterministic systems.
