Repository: Freie Universität Berlin, Math Department

# From Metastable to Coherent Sets – time-discretization schemes

Fackeldey, K. and Koltai, P. and Névir, P. and Rust, H.W. and Schild, A and Weber, M. (2019) From Metastable to Coherent Sets – time-discretization schemes. Chaos: An Interdisciplinary Journal of Nonlinear Science, 29 (1). 012101. ISSN 1054-1500 (print); 1089-7682 (online)

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Official URL: https://dx.doi.org/10.1063/1.5058128

## Abstract

Given a time-dependent stochastic process with trajectories x(t) in a space \Omega, there may be sets such that the corresponding trajectories only very rarely cross the boundaries of these sets. We can analyze such a process in terms of metastability or coherence. Metastable sets M are defined in space M \subset \Omega, coherent sets M(t) \subset \Omega are defined in space and time. Hence, if we extend the space \Omega by the time-variable t, coherent sets are metastable sets in \Omega \times [0,\infty). This relation can be exploited, because there already exist spectral algorithms for the identification of metastable sets. In this article we show that these well-established spectral algorithms (like PCCA+) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-time-discretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application.

Item Type: Article SFB 1114 Preprint: 12/2017 (p.1-13) Mathematical and Computer Sciences > Mathematics > Applied Mathematics Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group 2154 Silvia Hoemke 08 Dec 2017 09:41 31 Jan 2019 16:04

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