Article

Approximation of dynamical systems using s-systems theory: application to biological systems

Author:

Laurent TournierAuthors Info & Claims

ISSAC '05: Proceedings of the 2005 international symposium on Symbolic and algebraic computation

Pages 317 - 324

https://doi.org/10.1145/1073884.1073928

Published: 24 July 2005 Publication History

Abstract

In this article we propose a new symbolic-numeric algorithm to find positive equilibria of a n-dimensional dynamical system. This algorithm uses a symbolic manipulation of ODE in order to give a local approximation of differential equations with power-law dynamics (S-systems). A numerical calculus is then performed to converge towards an equilibrium, giving at the same time a S-system approximating the initial system around this equilibrium. This algorithm has been applied to a real biological example in 14 dimensions which is a subsystem of a metabolic pathway in Arabidopsis Thaliana.

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Cited By

Dräger AZielinski DKeller RRall MEichner JPalsson BZell A(2015)SBMLsqueezer 2: context-sensitive creation of kinetic equations in biochemical networksBMC Systems Biology10.1186/s12918-015-0212-99:1Online publication date: 9-Oct-2015
https://doi.org/10.1186/s12918-015-0212-9
Rosenfeld S(2009)Characteristics of Transcriptional Activity in Nonlinear Dynamics of Genetic Regulatory NetworksGene Regulation and Systems Biology10.4137/GRSB.S31193(GRSB.S3119)Online publication date: 19-Oct-2009
https://doi.org/10.4137/GRSB.S3119
Rosenfeld S(2009)Patterns of Stochastic Behavior in Dynamically Unstable High-Dimensional Biochemical NetworksGene Regulation and Systems Biology10.4137/GRSB.S20783(GRSB.S2078)Online publication date: 29-Jan-2009
https://doi.org/10.4137/GRSB.S2078
Show More Cited By

Index Terms

Approximation of dynamical systems using s-systems theory: application to biological systems
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Nonlinear equations

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Published In

cover image ACM Conferences

ISSAC '05: Proceedings of the 2005 international symposium on Symbolic and algebraic computation

July 2005

388 pages

ISBN:1595930957

DOI:10.1145/1073884

General Chairs:
Xiao-Shan Gao
MMRC, Chinese Academy of Sciences, China
,
George Labahn
University of Waterloo, ON, Canada

Copyright © 2005 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 24 July 2005

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ISSAC05: International Symposium on Symbolic and Algebraic Computation

July 24 - 27, 2005

Beijing, China

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Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

Dräger AZielinski DKeller RRall MEichner JPalsson BZell A(2015)SBMLsqueezer 2: context-sensitive creation of kinetic equations in biochemical networksBMC Systems Biology10.1186/s12918-015-0212-99:1Online publication date: 9-Oct-2015
https://doi.org/10.1186/s12918-015-0212-9
Rosenfeld S(2009)Characteristics of Transcriptional Activity in Nonlinear Dynamics of Genetic Regulatory NetworksGene Regulation and Systems Biology10.4137/GRSB.S31193(GRSB.S3119)Online publication date: 19-Oct-2009
https://doi.org/10.4137/GRSB.S3119
Rosenfeld S(2009)Patterns of Stochastic Behavior in Dynamically Unstable High-Dimensional Biochemical NetworksGene Regulation and Systems Biology10.4137/GRSB.S20783(GRSB.S2078)Online publication date: 29-Jan-2009
https://doi.org/10.4137/GRSB.S2078
Rosenfeld S(2007)Stochastic cooperativity in non-linear dynamics of genetic regulatory networksMathematical Biosciences10.1016/j.mbs.2007.05.006210:1(121-142)Online publication date: Nov-2007
https://doi.org/10.1016/j.mbs.2007.05.006

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