publication . Preprint . 2020

Extending Transition Path Theory: Periodically-Driven and Finite-Time Dynamics

Helfmann, Luzie; Borrell, Enric Ribera; Schütte, Christof; Koltai, Péter;
Open Access English
  • Published: 18 Feb 2020
Abstract
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 quanti...
Subjects
free text keywords: Mathematics - Dynamical Systems, 60J22, 82C26, 60J45, 60J10
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