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Abstract:

Toric dynamical systems are known as complex balancing mass action systems in the mathematical chemistry literature, where many of their remarkable properties have been established. They include as special cases all deficiency zero systems and all detailed balancing systems. One feature is that the steady state locus of a toric dynamical system is a toric variety, which has a unique point within each invariant polyhedron. We develop the basic theory of toric dynamical systems in the context of computational algebraic geometry and show that the associated moduli space is also a toric variety. It is conjectured that the complex balancing state is a global attractor. We prove this for detailed balancing systems whose invariant polyhedron is two-dimensional and bounded. © 2009 Elsevier Ltd. All rights reserved.

Registro:

Documento: Artículo
Título:Toric dynamical systems
Autor:Craciun, G.; Dickenstein, A.; Shiu, A.; Sturmfels, B.
Filiación:Department of Mathematics, University of Wisconsin, Madison, WI 53706-1388, United States
Dep. de Matemática, FCEN, Universidad de Buenos Aires, C1428EGA, Argentina
Department of Mathematics, University of California, Berkeley, CA 94720-3840, United States
Palabras clave:Birch's Theorem; Chemical reaction network; Complex balancing; Deficiency zero; Detailed balancing; Matrix-tree theorem; Moduli space; Polyhedron; Toric ideal; Trajectory
Año:2009
Volumen:44
Número:11
Página de inicio:1551
Página de fin:1565
DOI: http://dx.doi.org/10.1016/j.jsc.2008.08.006
Título revista:Journal of Symbolic Computation
Título revista abreviado:J. Symb. Comput.
ISSN:07477171
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_07477171_v44_n11_p1551_Craciun.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v44_n11_p1551_Craciun

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Citas:

---------- APA ----------
Craciun, G., Dickenstein, A., Shiu, A. & Sturmfels, B. (2009) . Toric dynamical systems. Journal of Symbolic Computation, 44(11), 1551-1565.
http://dx.doi.org/10.1016/j.jsc.2008.08.006
---------- CHICAGO ----------
Craciun, G., Dickenstein, A., Shiu, A., Sturmfels, B. "Toric dynamical systems" . Journal of Symbolic Computation 44, no. 11 (2009) : 1551-1565.
http://dx.doi.org/10.1016/j.jsc.2008.08.006
---------- MLA ----------
Craciun, G., Dickenstein, A., Shiu, A., Sturmfels, B. "Toric dynamical systems" . Journal of Symbolic Computation, vol. 44, no. 11, 2009, pp. 1551-1565.
http://dx.doi.org/10.1016/j.jsc.2008.08.006
---------- VANCOUVER ----------
Craciun, G., Dickenstein, A., Shiu, A., Sturmfels, B. Toric dynamical systems. J. Symb. Comput. 2009;44(11):1551-1565.
http://dx.doi.org/10.1016/j.jsc.2008.08.006