  In this work we study the opinion formation in a voter-like model defined on
a square lattice of linear size $L$. The agents may be in three different
states, representing any public debate with three choices (yes, no, undecided).
We consider heterogeneous agents that have different convictions about their
opinions. These convictions limit the capacity of persuasion of the individuals
during the interactions. Moreover, there is a noise $p$ that represents the
probability of an individual spontaneously change his opinion to the undecided
state. Our simulations suggest that the system reaches stationary states for
all values of $p$, with consensus states occurring only for the noiseless case
$p=0$. In this case, the relaxation times are distributed according to a
log-normal function, with the average value $\tau$ growing with the lattice
size as $\tau\sim L^{\alpha}$, where $\alpha\approx$ 0.9. We found a threshold
value $p^{*}\approx$ 0.9 above which the stationary fraction of undecided
agents is greater than the fraction of decided ones. We also study the
consequences of the presence of external effects in the system, which models
the influence of mass media on opinion formation.
