  We present results of direct numerical simulations on homoclinic gluing and
ungluing bifurcations in low-Prandtl-number ($ 0 \leq Pr \leq 0.025 $)
Rayleigh-B\'{e}nard system rotating slowly and uniformly about a vertical axis.
We have performed simulations with \textit{stress-free} top and bottom
boundaries for several values of Taylor number ($5 \leq Ta \leq 50$) near the
instability onset. We observe a single homoclinic ungluing bifurcation, marked
by the spontaneous breaking of a larger limit cycle into two limit cycles with
the variation of the reduced Rayleigh number $r$ for smaller values of $Ta (<
25)$. A pair of homoclinic bifurcations, instead of one bifurcation, is
observed with variation of $r$ for slightly higher values of $Ta$ ($25 \leq Ta
\leq 50$) in the same fluid dynamical system. The variation of the bifurcation
threshold with $Ta$ is also investigated. We have also constructed a
low-dimensional model which qualitatively captures the dynamics of the system
near the homoclinic bifurcations for low rotation rates. The model is used to
study the unfolding of bifurcations and the variation of the homoclinic
bifurcation threshold with $Pr$.
