Fackeldey, K. and Koltai, P. and Névir, P. and Rust, H.W. and Schild, A and Weber, M. (2019) From Metastable to Coherent Sets – timediscretization schemes. Chaos: An Interdisciplinary Journal of Nonlinear Science, 29 (1). 012101. ISSN 10541500 (print); 10897682 (online)

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Official URL: https://dx.doi.org/10.1063/1.5058128
Abstract
Given a timedependent 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 timevariable 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 wellestablished spectral algorithms (like PCCA+) also identify coherent sets of nonautonomous 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 spacetimediscretization scheme. The article gives an overview about different timediscretization schemes and shows their applicability in two different fields of application.
Item Type:  Article 

Additional Information:  SFB 1114 Preprint: 12/2017 (p.113) 
Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group 
ID Code:  2154 
Deposited By:  Silvia Hoemke 
Deposited On:  08 Dec 2017 09:41 
Last Modified:  31 Jan 2019 16:04 
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