Duality in mass-action networks

Abstract

Mass-action networks are special cases of chemical reaction networks. For these systems, we argue that conserved quantities are dual to internal cycles. We introduce maximal invariant polyhedral supports, and we conjecture that there is a duality relation between preclusters and maximal invariant polyhedral supports. Given the close relation between maximal invariant polyhedral supports and siphons, we also conjecture that siphons and preclusters are dual objects.

Figures (1)

• Figure 1: We chose $(c_1,c_2)$ to move on a segment $(c_1,c_2)\in\{(1-t,t)|t\in[0,1]\}$. The invariant polyhedron ${\mathcal{P}}_{\mathbf c}$ changes with $t$: we start with a triangle (fig. a), which becomes a quadrilateral (fig. b), which then becomes a triangle (fig. c and d), which collapses to a point (fig. e); eventually, ${\mathcal{P}}_{\mathbf c}$ becomes empty (fig. f).

Theorems & Definitions (25)

• Definition 1
• Example 2
• Remark 3
• Definition 4
• Remark 5
• Example 6
• Remark 7
• Example 8
• Example 9
• Remark 10