  We apply phase space analysis to inhomogeneous cosmological model given by
Lema\^itre-Tolman model. We describe some general conditions required to
interpret the model stable enough and, in the present paper, apply them to two
special cases: dust filled homogeneous model with and without cosmological
constant. We find that such stability explaining all present astrophysical
observations can not be achieved due to instabilities in phase space. This
hints that non-homogeneous models are not likely to be physically viable,
although any conclusive analysis requires more realistic modeling of
non-homogeneous universe.
