  The local stability of stellar and fluid discs, under a new modified
dynamical model, is surveyed by using WKB approximation. The exact form of the
modified Toomre criterion is derived for both types of systems and it is shown
that the new model is, in all situations, more locally stable than Newtonian
model. In addition, it has been proved that the central surface density of the
galaxies plays an important role in the local stability in the sense that LSB
galaxies are more stable than HSBs. Furthermore, the growth rate in the new
model is found to be lower than the Newtonian one. We found that, according to
this model, the local instability is related to the ratio of surface density of
the disc to a critical surface density $\Sigma^{crit}$. We provide
observational evidence to support this result based on star formation rate in
HSBs and LSBs.
