This study proposes mathematical models for functional differentiations that are viewed as self-organization with external constraints. From the viewpoint of system development, the present study investigates how system components emerge under the presence of constraints that act on a whole system. Cell differentiation in embryos and functional differentiation in cortical modules are typical examples of this phenomenon. In this paper, as case studies, we deal with three mathematical models that yielded components via such global constraints: the genesis of neuronal elements, the genesis of functional modules, and the genesis of neuronal interactions. The overall development of a system may follow a certain variational principle.