  Coherent properties of a two dimensional spatially periodic structure -
polaritonic crystal (PolC) formed by trapped two-level atoms in an optical
cavity array interacting with a light field, are analyzed. By considering the
wave function overlapping both for photonic and atomic states, a cubic-quintic
complex nonlinear Schrodinger equation (CNLSE) is derived for the dynamics of
coupled atom-light states - wave function of low branch (LB) polaritons,
associated with PolC in the continuous limit. The variational approach predicts
that a stable ground state wave function of PolC exists but is accompanied by
an oscillating width. For a negative scattering length, the wave function
collapses in the presence of a small quintic nonlinearity appear due to a three
body polariton interaction. Studying non-equilibrium (dissipative) dynamics of
polaritons with adiabatic approximation we have shown that the collapse of PolC
wave function can be prevented even in the presence of small decaying of a
number of polariton particles.
