  Very often, models in biology, chemistry, physics, and engineering are
systems of polynomial or power-law ordinary differential equations, arising
from a reaction network. Such dynamical systems can be generated by many
different 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.
