The Global Attractor Conjecture for complex-balanced mass action systems

A mass action system is a chemical reaction network whose reaction rates follow the mass action law; a stoichiometric compatibility class is a minimally invariant affine subset determined by the reaction vectors, and it is positive when it intersects the positive orthant. A steady state is complex-balanced when, at every reaction-network complex, the total incoming and outgoing reaction rates agree.

Global Attractor Conjecture. The unique complex-balanced steady state in each positive stoichiometric compatibility class of a complex-balanced mass action system is a global attractor of its respective compatibility class.

This is one of the central open problems in chemical reaction network theory. It is known in several special cases, including compatibility classes of dimension at most three and networks with a single linkage class; the general conjecture remains open.