A graph-theoretical approach for the analysis and model reduction of complex-balanced chemical reaction networks

Rao, Shodhan; Schaft, A.J. van der; Jayawardhana, Bayu

doi:10.1007/s10910-013-0218-8

Cited by 56 publications

(82 citation statements)

References 25 publications

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“…We remark that the number of complexes for CRNs realizing a given dynamics can also be minimized using the MILP method described in [29] which can be considered as a kind of model reduction. This result is related to [23], where the number of complexes of a complex-balanced CRN is reduced while maintaining the complex balance property and keeping a strong relation between the equilibria of the original and the reduced system.…”

Section: Let Us Use the Notation W = Im(y T ) + Ker(b T G ) Clearlymentioning

confidence: 97%

Computing zero deficiency realizations of kinetic systems

Lipták

Szederkényi

Hangos

2015

Systems & Control Letters

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In the literature, there exist strong results on the qualitative dynamical properties of chemical reaction networks (also called kinetic systems) governed by the mass action law and having zero deficiency. However, it is known that different network structures with different deficiencies may correspond to the same kinetic differential equations. In this paper, an optimization-based approach is presented for the computation of deficiency zero reaction network structures that are linearly conjugate to a given kinetic dynamics. Through establishing an equivalent condition for zero deficiency, the problem is traced back to the solution of an appropriately constructed mixed integer linear programming problem. Furthermore, it is shown that weakly reversible deficiency zero realizations can be determined in polynomial time using standard linear programming. Two examples are given for the illustration of the proposed methods.

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Section: Let Us Use the Notation W = Im(y T ) + Ker(b T G ) Clearlymentioning

confidence: 97%

Computing zero deficiency realizations of kinetic systems

Lipták

Szederkényi

Hangos

2015

Systems & Control Letters

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“…The reduced networked passive systemΣ in (21) preserves synchronization, i.e., when u = 0, it holds that (22) for any initial conditionx(0).…”

Section: Theorem 13mentioning

confidence: 99%

“…However, the application of this approach is only applicable to a tree topology. Another method based on singular perturbation is developed for reducing network complexity, which is mainly applied to electrical grids and chemical reaction networks (see e.g., [8,18,22]). In these works, the network structure is preserved as the Schur complement of the Laplacian matrix of the original network is again a Laplacian matrix, representing a smaller-scale network.…”

Section: Introductionmentioning

confidence: 99%

Balanced truncation of networked linear passive systems

2019

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This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of specifically selected generalized Gramians is implemented on the asymptotically stable part of the full-order network model, which leads to a reduced-order system preserving the passivity of each subsystem. Moreover, it is proven that there exists a coordinate transformation to convert the resulting reduced-order model to a state-space model of Laplacian dynamics. Thus, the proposed method simultaneously reduces the complexity of the network structure and individual agent dynamics, and it preserves the passivity of the subsystems and the synchronization of the network. Moreover, it allows for the a priori computation of a bound on the approximation error. Finally, the feasibility of the method is demonstrated by an example. (Xiaodong Cheng), j.m.a.scherpen@rug.nl (Jacquelien M.A. Scherpen), b.besselink@rug.nl (Bart Besselink).

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“…In order to carry out the analysis we need to first introduce some preliminaries on chemical reaction networks using the concept of graph of complexes from [10], [15] and [8].…”

Section: Complex-balanced Ss Network With Fixed Boundary Concenmentioning

confidence: 99%

“…Complexes are the left and right hand sides of the reactions of a network and a complex-balanced reaction network is one for which there exists a vector of species concentrations at which the combined rate of outgoing reactions from any complex is equal to the combined rate of incoming reactions to the complex. The notion of complex-balanced networks was first introduced in [4] and studied in detail in [5], [6], [7], [8], [9], [10]. Network (1) is an example of a SS complex balanced network.…”

Section: Introductionmentioning

confidence: 99%

Analysis of complex balanced chemical reaction networks with fixed boundary concentrations

Rao

Schaft

Jayawardhana

2013

52nd IEEE Conference on Decision and Control

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In this paper, we analyze the dynamics of complex balanced single-substrate single-product (SS) chemical reaction networks governed by mass-action kinetics with a carefully chosen set of boundary species fixed at constant concentrations. The remaining species of the reaction networks are allowed to have constant influx and/or proportional efflux. We show that such a network has a unique equilibrium concentration vector in the positive orthant and it is asymptotically stable. Using the maximum modulus principle for graphs, we provide bounds for this equilibrium

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A graph-theoretical approach for the analysis and model reduction of complex-balanced chemical reaction networks

Cited by 56 publications

References 25 publications

Computing zero deficiency realizations of kinetic systems

Computing zero deficiency realizations of kinetic systems

Balanced truncation of networked linear passive systems

Analysis of complex balanced chemical reaction networks with fixed boundary concentrations

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