  We analyze in detail the quantum phase transitions that arise in models based
on the $u(2)$ algebraic description for bosonic systems with two types of
scalar bosons. First we discuss the quantum phase transition that occurs in
hamiltonians that admix the two dynamical symmetry chains $u(2)\supset u(1)$
and $u(2)\supset so(2)$ by diagonalizing the problem exactly in the $u(1)$
basis. Then we apply the coherent state formalism to determine the energy
functional. Finally we show that a quantum phase transition of a different
nature, but displaying similar characteristics, may arise also within a single
chain just by including higher order terms in the hamiltonian.
