  The non-singular bouncing cosmology is an alternative paradigm to inflation,
wherein the background energy density vanishes at the bounce point, in the
context of Einstein gravity. Therefore, the non-linear effects in the evolution
of density fluctuations ($\delta \rho$) may be strong in the bounce phase,
which potentially provides a mechanism to enhance the abundance of primordial
black holes (PBHs). This article presents a comprehensive illustration for PBH
enhancement due to the bounce phase. To calculate the non-linear evolution of
$\delta \rho$, the Raychaudhuri equation is numerically solved here. Since the
non-linear processes may lead to a non-Gaussian probability distribution
function for $\delta \rho$ after the bounce point, the PBH abundance is
calculated in a modified Press-Schechter formalism. In this case, the criterion
of PBH formation is complicated, due to complicated non-linear evolutionary
behavior of $\delta \rho$ during the bounce phase. Our results indicate that
the bounce phase indeed has potential to enhance the PBH abundance
sufficiently. Furthermore, the PBH abundance is applied to constrain the
parameters of bounce phase, providing a complementary to the surveys of cosmic
microwave background and large scale structure.
