  We investigate the stability of nearby disc galaxies and galaxies at redshift
($z$) equal to 4.5. We explore the connection between the stability parameter
$(Q_{RW})$, star formation rate ($SFR$), gas fraction $(f^{Gas})$, and the time
scale for growth of gravitational instabilities $(\tau)$. We find that, despite
differences in morphology $91$ $\%$ of the nearby galaxies have a minimum value
of stability parameter ($Q^{Min}_{RW}$) greater than $1$ indicating stability
against the growth of axisymmetric instabilities. The spirals in our sample
have higher median star formation rate, lower median $Q_{RW}$, a lower
$f^{Gas}$ and small time scale for growth of gravitational instabilities than
irregular galaxies. We find that the gravitational instabilities in spirals
convert a large fraction of gas into stars quickly, depleting the gas
reservoirs. On the other hand, star formation occurs more gradually over longer
timescales in irregulars with a higher gas fraction. We then compare the
stability of the nearby galaxies with galaxies at $z\,=\,4.5$. We find that net
stability levels in the nearby galaxies and the galaxies at $z\,=\,4.5$ are
primarily driven by the stellar disc suggesting the presence of an inherent
mechanism that self-regulates the stability. Finally, upon removing the
contribution of the dark matter to the total potential, the median $Q_{RW}$ for
the nearby galaxies and galaxies at $z \,= \,4.5$ remains unchanged indicating
that the baryons can self-regulate the stability levels, at least in a
statistical sense.
