Bittracher, A. and Koltai, P. and Klus, S. and Banisch, R. and Dellnitz, M. and Schütte, Ch. (2017) Transition manifolds of complex metastable systems: Theory and datadriven computation of effective dynamics. Journal of Nonlinear Science . pp. 142. ISSN 14321467 (online)

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Official URL: http://dx.doi.org/10.1007/s0033201794150
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 lowdimensional 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 lowdimensional 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 databased model reduction of complex dynamical systems such as molecular dynamics.
Item Type:  Article 

Additional Information:  SFB 1114 Preprint: 04/2017 in arXiv1704.08927 
Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group 
ID Code:  2138 
Deposited By:  Silvia Hoemke 
Deposited On:  27 Nov 2017 14:08 
Last Modified:  28 Nov 2017 10:02 
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