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

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 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.

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Cited by in corpus (12)

• Transition paths of marine debris and the stability of the garbage patches
• Dynamical geography and transition paths of Sargassum in the tropical Atlantic
• Data-driven methods to estimate the committor function in conceptual ocean models
• Variational deep learning of equilibrium transition path ensembles
• Statistical Analysis of Tipping Pathways in Agent-Based Models
• Transition paths of North Atlantic Deep Water
• Augmented Transition Path Theory for Sequences of Events
• Data-driven transition path analysis yields a statistical understanding of sudden stratospheric warming events in an idealized model
• Stability of temporal statistics in Transition Path Theory with sparse data
• Sampling--Dependent Transition Paths of Iceland-Scotland Overflow Water
• Tracing the origin of tropical North Atlantic Sargassum blooms to West Africa
• The Augmented Jump Chain -- a sparse representation of time-dependent Markov jump processes