[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14317/jami.2011.29.3_4.949

REMARKS ON CRITERIA FOR THE EXISTENCE OF A POSITIVE EQUILIBRIUM IN REACTION NETWORKS

Choo, S.M. (Department of Mathematics, University of Ulsan)

Publication Information

Journal of applied mathematics & informatics / v.29, no.3_4, 2011 , pp. 949-953 More about this Journal

Abstract

It is interesting to know the behavior of a network from its structure. One interesting topic is to find a relation between the existence of a positive equilibrium of the reaction network and its structure. One approach to study this topic is using the concept of deficiency. Another is using some conditions on nodes, which can apply to large-size networks compared to deficiency. In this work, we show the relation between deficiency and the conditions.

Keywords

Differential equation; reaction equation; positive equilibrium; reaction network; deficiency; rank;

Citations & Related Records

Reference

1	S.M. Choo and N.Y. Lee, New criteria for the existence of a positive equilibrium in reaction networks, Appl. Math. Lett., 24(2011), 450-453. DOI ScienceOn
2	S.Y. Shin, O. Rath, S.M. Choo, F. Fee, B. McFerran, W. Kolch, and K.H. Cho, Positive- and negative-feedback regulations coordinate the dynamic behavior of the Ras-Raf-MEK-ERK signal transduction pathway, J Cell Sci. 122(2009), 425-435 DOI ScienceOn
3	G. Craciun and M. Feinberg, Multiple equilibria in complex chemical reaction networks: II. The species-reaction graph, SIAM J. Appl. Math. 66(2006), 1321 - 1338. DOI ScienceOn
4	M. Feinberg, The existence and uniqueness of steady states for a class of chemical reaction networks, Arch. Rational Mech. Anal. 132(1995), 311 - 370 DOI ScienceOn
5	J. Gunawardena, Chemical reaction network theory for in-silico biologists, Lecture notes, Bauer Center for Genomics Research, Harvard University, 2003.
6	N.I. Markevich, J.B. Hoek, and B.N. Kholodenko,Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades, J Cell Biol. 164(3)(2004), 353- 359. DOI ScienceOn
7	M. Banaji, P. Donnell and S. Baigent, P matrix properties, injectivity, and stability in chemical reaction systems, SIAM J. Appl. Math.67(2007), 1523 - 1547. DOI ScienceOn