An efficient characterization of complex-balanced, detailed-balanced, and weakly reversible systems

Very often, models in biology, chemistry, physics, and engineering are systems of polynomial or power-law ordinary difierential equations, arising from a reaction network. Such dynamical systems can be generated by many difierent reaction networks. On the other hand, networks with special properties (such as reversibility or weak reversibility) are known or conjectured to give rise to dynamical systems that have special properties: Existence of positive steady states, persistence, permanence, and (for well-chosen parameters) complex balancing or detailed balancing. These last two are related to thermodynamic equilibrium, and therefore the positive steady states are unique and stable. We describe a computationally efficient characterization of polynomial or power-law dynamical systems that can be obtained as complex-balanced, detailed-balanced, weakly reversible, and reversible mass-action systems.