Name
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. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1016/j.jsc.2008.08.006 | J. Symb. Comput. |
Keywords | DocType | Volume |
detailed balancing system,invariant polyhedron,Matrix-tree theorem,polyhedron,complex balancing mass action,complex balancing,Toric ideal,moduli space,toric ideal,complex balancing state,toric dynamical system,Moduli space,Chemical reaction network,Birch’s Theorem,basic theory,associated moduli space,toric variety,chemical reaction network,computational algebraic geometry,detailed balancing,matrix-tree theorem,Complex balancing,Detailed balancing,trajectory,birch's theorem,steady state locus,deficiency zero,Polyhedron,Deficiency zero,Trajectory | Journal | 44 |
Issue | ISSN | Citations |
11 | Journal of Symbolic Computation | 16 |
PageRank | References | Authors |
1.51 | 2 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gheorghe Craciun | 1 | 185 | 34.23 |
| Alicia Dickenstein | 2 | 115 | 14.88 |
| Anne Shiu | 3 | 87 | 14.47 |
| Bernd Sturmfels | 4 | 926 | 136.85 |