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Volumn 43, Issue 4, 2009, Pages 394-414

Univalent positive polynomial maps and the equilibrium state of chemical networks of reversible binding reactions

Author keywords

Chemical reaction network; Complete network; Detailed balance; Equilibrium; Global univalence; Normal network; P matrix; Reversible binding reaction

Indexed keywords

CHEMICAL REACTION NETWORK; COMPLETE NETWORK; DETAILED BALANCE; EQUILIBRIUM; GLOBAL UNIVALENCE; NORMAL NETWORK; P-MATRIX; REVERSIBLE BINDING REACTION;

EID: 69849107725     PISSN: 01968858     EISSN: 10902074     Source Type: Journal    
DOI: 10.1016/j.aam.2009.05.001     Document Type: Article
Times cited : (18)

References (34)
  • 2
    • 37849018685 scopus 로고    scopus 로고
    • P matrix properties, injectivity, and stability in chemical reaction systems
    • Banaji M., Donnell P., and Baigent S. P matrix properties, injectivity, and stability in chemical reaction systems. SIAM J. Appl. Math. 67 (2007) 1523-1547
    • (2007) SIAM J. Appl. Math. , vol.67 , pp. 1523-1547
    • Banaji, M.1    Donnell, P.2    Baigent, S.3
  • 3
    • 0003270351 scopus 로고
    • Nonnegative Matrices in the Mathematical Sciences
    • SIAM, Philadelphia
    • Berman A., and Plemmons R.J. Nonnegative Matrices in the Mathematical Sciences. Classics Appl. Math. vol. 9 (1994), SIAM, Philadelphia
    • (1994) Classics Appl. Math. , vol.9
    • Berman, A.1    Plemmons, R.J.2
  • 4
    • 84883937488 scopus 로고    scopus 로고
    • Positive Definite Matrices
    • Princeton Univ. Press, Princeton
    • Bhatia R. Positive Definite Matrices. Princeton Ser. Appl. Math. (2007), Princeton Univ. Press, Princeton
    • (2007) Princeton Ser. Appl. Math.
    • Bhatia, R.1
  • 6
    • 2942694522 scopus 로고    scopus 로고
    • How to impose microscopic reversibility in complex reaction mechanisms
    • Colquhoun D., Dowsland K.A., Beato M., and Plested A.J.R. How to impose microscopic reversibility in complex reaction mechanisms. Biophys. J. 86 (2004) 3510-3518
    • (2004) Biophys. J. , vol.86 , pp. 3510-3518
    • Colquhoun, D.1    Dowsland, K.A.2    Beato, M.3    Plested, A.J.R.4
  • 8
    • 69849109642 scopus 로고    scopus 로고
    • private communication, July
    • G. Craciun, private communication, July 2007
    • (2007)
    • Craciun, G.1
  • 9
    • 68549135061 scopus 로고    scopus 로고
    • G. Craciun, A. Dickenstein, A. Shiu, B. Sturmfels, Toric Dynamical Systems, J. Symbolic Comput. (2009), doi:10.1016/j.jsc.2008.08.006, in press
    • G. Craciun, A. Dickenstein, A. Shiu, B. Sturmfels, Toric Dynamical Systems, J. Symbolic Comput. (2009), doi:10.1016/j.jsc.2008.08.006, in press
  • 10
    • 27844475135 scopus 로고    scopus 로고
    • Multiple equilibria in complex chemical reaction networks: I. The injectivity property
    • Craciun G., and Feinberg M. Multiple equilibria in complex chemical reaction networks: I. The injectivity property. SIAM J. Appl. Math. 65 (2005) 1526-1546
    • (2005) SIAM J. Appl. Math. , vol.65 , pp. 1526-1546
    • Craciun, G.1    Feinberg, M.2
  • 12
    • 69849113910 scopus 로고    scopus 로고
    • private communication, July
    • G. Di Lena, private communication, July 2008
    • (2008)
    • Di Lena, G.1
  • 13
    • 0015482348 scopus 로고
    • Complex balancing in general kinetic systems
    • Feinberg M. Complex balancing in general kinetic systems. Arch. Ration. Mech. Anal. 49 (1972) 187-194
    • (1972) Arch. Ration. Mech. Anal. , vol.49 , pp. 187-194
    • Feinberg, M.1
  • 15
    • 0001364051 scopus 로고
    • The existence and uniqueness of steady states for a class of chemical reaction networks
    • Feinberg M. The existence and uniqueness of steady states for a class of chemical reaction networks. Arch. Ration. Mech. Anal. 132 (1995) 311-370
    • (1995) Arch. Ration. Mech. Anal. , vol.132 , pp. 311-370
    • Feinberg, M.1
  • 16
    • 0342620694 scopus 로고
    • The Jacobian matrix and global univalence of mappings
    • Gale D., and Nikaidô H. The Jacobian matrix and global univalence of mappings. Math. Ann. 159 (1965) 81-93
    • (1965) Math. Ann. , vol.159 , pp. 81-93
    • Gale, D.1    Nikaidô, H.2
  • 21
    • 0015489310 scopus 로고
    • Necessary and sufficient conditions for complex balancing in chemical kinetics
    • Horn F. Necessary and sufficient conditions for complex balancing in chemical kinetics. Arch. Ration. Mech. Anal. 49 (1972) 172-186
    • (1972) Arch. Ration. Mech. Anal. , vol.49 , pp. 172-186
    • Horn, F.1
  • 22
    • 0004433445 scopus 로고
    • The dynamics of open reaction systems
    • Mathematical Aspects of Chemical and Biochemical Problems and Quantum Chemistry, Amer. Math. Soc., Providence, RI
    • Horn F. The dynamics of open reaction systems. Mathematical Aspects of Chemical and Biochemical Problems and Quantum Chemistry. SIAM-AMS Proc. vol. 8 (1974), Amer. Math. Soc., Providence, RI 125-137
    • (1974) SIAM-AMS Proc. , vol.8 , pp. 125-137
    • Horn, F.1
  • 28
    • 0012722590 scopus 로고    scopus 로고
    • Iterative Solution of Nonlinear Equations in Several Variables
    • SIAM, Philadelphia
    • Ortega J.M., and Rheinboldt W.C. Iterative Solution of Nonlinear Equations in Several Variables. Classics Appl. Math. vol. 30 (2000), SIAM, Philadelphia
    • (2000) Classics Appl. Math. , vol.30
    • Ortega, J.M.1    Rheinboldt, W.C.2
  • 29
    • 0003290691 scopus 로고
    • On Global Univalence Theorems
    • Springer-Verlag, Berlin
    • Parthasarathy T. On Global Univalence Theorems. Lecture Notes in Math. vol. 977 (1983), Springer-Verlag, Berlin
    • (1983) Lecture Notes in Math. , vol.977
    • Parthasarathy, T.1
  • 30
    • 58449106508 scopus 로고    scopus 로고
    • Sensitivity and robustness in chemical reaction networks
    • Shinar G., Alon U., and Feinberg M. Sensitivity and robustness in chemical reaction networks. SIAM J. Appl. Math. 69 (2009) 977-998
    • (2009) SIAM J. Appl. Math. , vol.69 , pp. 977-998
    • Shinar, G.1    Alon, U.2    Feinberg, M.3
  • 31
    • 0000058258 scopus 로고
    • Global stability of deficiency zero chemical networks
    • Siegel D., and Chen Y.F. Global stability of deficiency zero chemical networks. Can. Appl. Math. Q. 2 (1994) 413-434
    • (1994) Can. Appl. Math. Q. , vol.2 , pp. 413-434
    • Siegel, D.1    Chen, Y.F.2
  • 32
    • 0003270907 scopus 로고
    • Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems
    • Amer. Math. Soc., Providence, RI
    • Smith H.L. Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems. Math. Surveys Monogr. vol. 41 (1995), Amer. Math. Soc., Providence, RI
    • (1995) Math. Surveys Monogr. , vol.41
    • Smith, H.L.1
  • 33
    • 7744230024 scopus 로고    scopus 로고
    • Graphic requirements for multistationarity
    • Soulé C. Graphic requirements for multistationarity. ComPlexUs 1 (2003) 123-133
    • (2003) ComPlexUs , vol.1 , pp. 123-133
    • Soulé, C.1
  • 34
    • 0039504336 scopus 로고
    • Analysis in Classes of Discontinuous Functions and Equations of Mathematical Physics
    • Springer-Verlag, Berlin
    • Vol'pert A.I., and Hudjaev S.I. Analysis in Classes of Discontinuous Functions and Equations of Mathematical Physics. Mechanics: Analysis vol. 8 (1985), Springer-Verlag, Berlin
    • (1985) Mechanics: Analysis , vol.8
    • Vol'pert, A.I.1    Hudjaev, S.I.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.