  We study cosmological evolutions of the generalized model of nonlinear
massive gravity in which the graviton mass is given by a rolling scalar field
and is varying along time. By performing dynamical analysis, we derive the
critical points of this system and study their stabilities. These critical
points can be classified into two categories depending on whether they are
identical with the traditional ones obtained in General Relativity. We discuss
the cosmological implication of relevant critical points.
