The Global Attractor Conjecture for detailed balanced reaction systems

Consider a reversible reaction system and a detailed balanced equilibrium, meaning an equilibrium satisfying detailed balance for every reversible reaction. A trajectory is a solution of the corresponding mass-action dynamical system, and its initial concentrations are strictly positive when every concentration is positive. Global Attractor Conjecture. If the reaction system has a detailed balanced equilibrium, then every trajectory starting from strictly positive initial concentrations reaches it in the limit. The conjecture seeks a global convergence theorem for detailed balanced mass-action systems: the equilibria are known to be local attractors, but the asserted convergence of every positive trajectory remains open and is described in the source as a fundamental open question.