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Entropy 2010, 12(4), 706-719; doi:10.3390/e12040706
Article

Entropy-Related Extremum Principles for Model Reduction of Dissipative Dynamical Systems

1,2
1 Center for Systems Biology (ZBSA), University of Freiburg, Habsburgerstraße 49, 79104 Freiburg, Germany 2 Interdisciplinary Center for Scientific Computing (IWR), University of Heidelberg, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany
Received: 12 February 2010 / Revised: 23 March 2010 / Accepted: 1 April 2010 / Published: 1 April 2010
(This article belongs to the Special Issue Entropy in Model Reduction)
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Abstract

Chemical kinetic systems are modeled by dissipative ordinary differential equations involving multiple time scales. These lead to a phase flow generating anisotropic volume contraction. Kinetic model reduction methods generally exploit time scale separation into fast and slow modes, which leads to the occurrence of low-dimensional slow invariant manifolds. The aim of this paper is to review and discuss a computational optimization approach for the numerical approximation of slow attracting manifolds based on entropy-related and geometric extremum principles for reaction trajectories.
Keywords: model reduction; slow invariant manifolds; chemical kinetics; extremum principles; entropy concepts model reduction; slow invariant manifolds; chemical kinetics; extremum principles; entropy concepts
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Lebiedz, D. Entropy-Related Extremum Principles for Model Reduction of Dissipative Dynamical Systems. Entropy 2010, 12, 706-719.

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