Helfmann, Luzie and Ribera Borrell, Enric and Schütte, Christof and Koltai, Péter
(2020)
*Extending Transition Path Theory: Periodically Driven and
Finite-Time Dynamics.*
Journal of Nonlinear Science
.
pp. 1-46.
ISSN 1432-1467 (online)

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Official URL: https://doi.org/10.1007/s00332-020-09652-7

## Abstract

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.

Item Type: | Article |
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Subjects: | Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group |

ID Code: | 2591 |

Deposited By: | Monika Drueck |

Deposited On: | 27 Aug 2021 13:26 |

Last Modified: | 25 Oct 2021 20:36 |

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