Toric dynamical systems

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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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Autores principales:	Craciun, G., Dickenstein, A., Shiu, A., Sturmfels, B.
Formato:	JOUR
Materias:	Birch's Theorem Chemical reaction network Complex balancing Deficiency zero Detailed balancing Matrix-tree theorem Moduli space Polyhedron Toric ideal Trajectory
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_07477171_v44_n11_p1551_Craciun
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_07477171_v44_n11_p1551_Craciun
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spelling	todo:paper_07477171_v44_n11_p1551_Craciun2023-10-03T15:38:56Z Toric dynamical systems 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. JOUR 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)
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	JOUR
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
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_	1807317570686025728

Toric dynamical systems

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