Toric dynamical systems
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...
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| Formato: | Artículo publishedVersion |
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2009
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_07477171_v44_n11_p1551_Craciun |
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paperaa:paper_07477171_v44_n11_p1551_Craciun2023-06-12T16:48:12Z Toric dynamical systems J. Symb. Comput. 2009;44(11):1551-1565 Craciun, G. Dickenstein, A. Shiu, A. Sturmfels, B. Birch's Theorem Chemical reaction network Complex balancing Deficiency zero Detailed balancing Matrix-tree theorem Moduli space Polyhedron Toric ideal Trajectory 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. Fil:Dickenstein, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2009 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_07477171_v44_n11_p1551_Craciun |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| language |
Inglés |
| orig_language_str_mv |
eng |
| topic |
Birch's Theorem Chemical reaction network Complex balancing Deficiency zero Detailed balancing Matrix-tree theorem Moduli space Polyhedron Toric ideal Trajectory |
| spellingShingle |
Birch's Theorem Chemical reaction network Complex balancing Deficiency zero Detailed balancing Matrix-tree theorem Moduli space Polyhedron Toric ideal Trajectory Craciun, G. Dickenstein, A. Shiu, A. Sturmfels, B. Toric dynamical systems |
| topic_facet |
Birch's Theorem Chemical reaction network Complex balancing Deficiency zero Detailed balancing Matrix-tree theorem Moduli space Polyhedron Toric ideal Trajectory |
| description |
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. |
| format |
Artículo Artículo publishedVersion |
| author |
Craciun, G. Dickenstein, A. Shiu, A. Sturmfels, B. |
| author_facet |
Craciun, G. Dickenstein, A. Shiu, A. Sturmfels, B. |
| author_sort |
Craciun, G. |
| title |
Toric dynamical systems |
| title_short |
Toric dynamical systems |
| title_full |
Toric dynamical systems |
| title_fullStr |
Toric dynamical systems |
| title_full_unstemmed |
Toric dynamical systems |
| title_sort |
toric dynamical systems |
| publishDate |
2009 |
| url |
http://hdl.handle.net/20.500.12110/paper_07477171_v44_n11_p1551_Craciun |
| work_keys_str_mv |
AT craciung toricdynamicalsystems AT dickensteina toricdynamicalsystems AT shiua toricdynamicalsystems AT sturmfelsb toricdynamicalsystems |
| _version_ |
1769810123192008704 |