  The properties of the collective low-lying states of Zr isotopes which
include excitation energies and $E2$ reduced transition probabilities indicate
that some of these states are mainly spherical and the other are mainly
deformed ones. We investigate the properties of the low-lying collective states
of $^{92-102}$Zr and their evolution with increase of the number of neutrons
based on the five-dimensional Geometrical Quadrupole Collective Model. The
quadrupole-collective Bohr Hamiltonian with a potential having spherical and
deformed minima, is applied. The relative depth of two minima, height and width
of the barrier, rigidity of the potential near both minima are determined so as
to achieve the best possible description of the observed properties of the
low-lying collective quadrupole states of $^{92-102}$Zr. Satisfactory agreement
with the experimental data on the excitation energies and the $E2$ reduced
transition probabilities is obtained. The evolution of the collective potential
with increase of $A$ is described and the distributions of the wave functions
of the collective states in $\beta-\gamma$ plane are found. The resulting
potential evolves with $A$ increase from having only one spherical minimum in
$^{92}$Zr, through the potentials having both spherical and deformed minima, to
the potential with one deformed minimum in $^{102}$Zr.
