Before revision:  In particular,  for deterministic models it is well known that weak reversibility and a deficiency zero of the reaction network imply that the model is complex balanced .
After revision:  In particular, for deterministic models , which date back to the early 1970s, focus on models with a deficiency of zero and connect them to detailed-balanced models. Moreover, the largest open conjecture related to deterministic models, the so-called Global Attractor Conjecture, focuses on models with a deficiency of zero .