Bittracher, A. and Koltai, P. and Klus, S. and Banisch, R. and Dellnitz, M. and Schütte, Ch.
(2018)
*Transition manifolds of complex metastable systems: Theory and data-driven computation of effective dynamics.*
Journal of Nonlinear Science, 28
(2).
pp. 471-512.
ISSN 1432-1467 (online)

Full text not available from this repository.

Official URL: https://link.springer.com/article/10.1007%2Fs00332...

## Abstract

We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics.

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

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

ID Code: | 2307 |

Deposited By: | BioComp Admin |

Deposited On: | 14 Mar 2019 13:09 |

Last Modified: | 14 Mar 2019 13:09 |

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