Toric dynamical systems

• Autores: Craciun, Gheorghe; Dickenstein, Alicia Marcela; Shiu, Anne; Sturmfels, Bernd
• Año de publicación: 2009
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: CHEMICAL REACTION NETWORK; TORIC IDEAL; COMPLEX BALANCING; DETAILED BALANCING; DEFICIENCY ZERO; TRAJECTORY; BIRCH’S THEOREM; MATRIX-TREE THEOREM; MODULI SPACE; POLYHEDRON
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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.
Fil: Craciun, Gheorghe. University of Wisconsin; Estados Unidos
Fil: Dickenstein, Alicia Marcela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Shiu, Anne. University of California at Berkeley; Estados Unidos
Fil: Sturmfels, Bernd. University of California at Berkeley; Estados Unidos