Characterization and partial synthesis of the behavior of resistive circuits at their terminals

Schaft, A.J. van der

doi:10.1016/j.sysconle.2010.05.005

Cited by 47 publications

(12 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We propose a novel method for model reduction of chemical reaction networks governed by enzyme kinetics. Our method is inspired by the Kron reduction method for model reduction of resistive electrical networks described in [ 25 ]; see also [ 32 ].…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

A model reduction method for biochemical reaction networks

et al. 2014

View full text Add to dashboard Cite

BackgroundIn this paper we propose a model reduction method for biochemical reaction networks governed by a variety of reversible and irreversible enzyme kinetic rate laws, including reversible Michaelis-Menten and Hill kinetics. The method proceeds by a stepwise reduction in the number of complexes, defined as the left and right-hand sides of the reactions in the network. It is based on the Kron reduction of the weighted Laplacian matrix, which describes the graph structure of the complexes and reactions in the network. It does not rely on prior knowledge of the dynamic behaviour of the network and hence can be automated, as we demonstrate. The reduced network has fewer complexes, reactions, variables and parameters as compared to the original network, and yet the behaviour of a preselected set of significant metabolites in the reduced network resembles that of the original network. Moreover the reduced network largely retains the structure and kinetics of the original model.ResultsWe apply our method to a yeast glycolysis model and a rat liver fatty acid beta-oxidation model. When the number of state variables in the yeast model is reduced from 12 to 7, the difference between metabolite concentrations in the reduced and the full model, averaged over time and species, is only 8%. Likewise, when the number of state variables in the rat-liver beta-oxidation model is reduced from 42 to 29, the difference between the reduced model and the full model is 7.5%.ConclusionsThe method has improved our understanding of the dynamics of the two networks. We found that, contrary to the general disposition, the first few metabolites which were deleted from the network during our stepwise reduction approach, are not those with the shortest convergence times. It shows that our reduction approach performs differently from other approaches that are based on time-scale separation. The method can be used to facilitate fitting of the parameters or to embed a detailed model of interest in a more coarse-grained yet realistic environment.

show abstract

Section: Methodsmentioning

confidence: 99%

“…( 1 .) Follows from the proof of ( [ 33 ], Theorem 3.11); see also [ 32 ] for the case of symmetric L . ( 2 .)…”

Section: Methodsmentioning

confidence: 99%

A model reduction method for biochemical reaction networks

et al. 2014

View full text Add to dashboard Cite

show abstract

“…Eq. ( 1) is in port-Hamiltonian input-state-output form ( van der Schaft, 1996;van der Schaft & Jeltsema, 2014;van der Schaft & Maschke, 1995 ) ˙…”

Section: Port-hamiltonian Modeling Of the Synchronous Generatorunclassified

“…Note that as always in a port-Hamiltonian formulation the partial derivatives of the Hamiltonian H have a direct physical interpretation ( Fiaz et al, 2013;van der Schaft, 1996;van der Schaft & Jeltsema, 2014;van der Schaft & Maschke, 1995 ). In fact,…”

Section: Port-hamiltonian Modeling Of the Synchronous Generatormentioning

confidence: 99%

“…This can be extended to shifted passivity with respect to any constant V f , V dq and τ = 0 as follows. The standard method ( Maschke, Ortega, & van der Schaft, 20 0 0;van der Schaft, 1996;van der Schaft & Jeltsema, 2014 ) of studying shifted passivity for a general port-Hamiltonian system ( 2) is based on adding to its Hamiltonian H a function determined by the input matrix g ( x ) and the complete structure matrix J(x ) − R (x ) , provided additional integrability conditions are satisfied ( Fiaz et al, 2013;Maschke et al, 20 0 0 ).…”

Section: Analysis Of the Synchronous Generator By The Blondel-park Transformationmentioning

confidence: 99%

See 1 more Smart Citation

Perspectives in modeling for control of power networks

Schaft

2016

Annual Reviews in Control

Self Cite

View full text Add to dashboard Cite

Structure-Preserving Model Reduction of Physical Network Systems

Schaft

2022

Realization and Model Reduction of Dynamical Systems

Self Cite

View full text Add to dashboard Cite

the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

show abstract

Characterization and partial synthesis of the behavior of resistive circuits at their terminals

Cited by 47 publications

References 13 publications

A model reduction method for biochemical reaction networks

A model reduction method for biochemical reaction networks

Perspectives in modeling for control of power networks

Structure-Preserving Model Reduction of Physical Network Systems

Contact Info

Product

Resources

About