  In this research note, I derive explicit dynamical systems for language
within an acquisition-driven framework (Niyogi \& Berwick, 1997; Niyogi, 2006)
assuming that children/learners follow the Tolerance Principle (Yang, 2016) to
determine whether a rule is productive during the process of language
acquisition. I consider different theoretical parameters such as population
size (finite vs. infinite) and the number of previous generations that provide
learners with data. Multiple simulations of the dynamics obtained here and
applications to diacrhonic language data are in preparation, so they are not
included in this first note.
