Toric dynamical systems
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 twodimensional and bounded.
 Publication:

arXiv eprints
 Pub Date:
 August 2007
 arXiv:
 arXiv:0708.3431
 Bibcode:
 2007arXiv0708.3431C
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematics  Algebraic Geometry
 EPrint:
 We include the proof of our Conjecture 5 (now Lemma 5) and add some references