What is the regulator system in a spring drive movement called?

The Tri-synchro regulator consists of the glide wheel, coil wound stators, and the IC and quarts oscillator package that constitute the actual regulating system.  In a Spring Drive movement, the glide wheel, stators and IC fulfil the functions of the escape wheel and lever in a conventional mechanical watch, while the role of the balance wheel is fulfilled by the quartz crystal.