  Wigner distribution function of atomic system interacts locally with a
deformed cavity is discussed. It is shown that, the deformed cavity has a
destructive effect on the Wigner distribution function, where it decreases as
one increases the deformation strength. The upper and lower bounds of the
Wigner distribution function depends on the initial state settings of atomic
system (entangled/product), the initial values of the dipole-dipole
interaction's and detuning parameters, and the external distribution weight and
the phase angles. The possibility of suppressing the decay induced by the
deformed cavity may be increased by increasing the dipole's strength or the
detuning parameter. We show that the distribution angles may be considered as a
control external parameters, that maximize/ minimize the Wigner distribution
function. This means that by controlling on the distribution angles, one can
increase the possibility of suppressing the decoherence induced by the deformed
cavity.
