  The pursuit of understanding the mysteries surrounding dark energy has
sparked significant interest within the field of cosmology. While conventional
approaches, such as the cosmological constant, have been extensively explored,
alternative theories incorporating scalar field-based models and modified
gravity have emerged as intriguing avenues. Among these, teleparallel theories
of gravity, specifically the $f(T,\phi)$ formulation, have gained prominence as
a means to comprehend dark energy within the framework of teleparallelism. In
this study, we investigate two well-studied models of teleparallel dark energy
and examine the presence of cosmological singularities within these scenarios.
Using the Goriely-Hyde procedure, we examine the dynamical systems governing
the cosmological equations of these models. Our analysis reveals that both
models exhibit Type IV singularities, but only for a limited range of initial
conditions. These results could indicate a potential edge for teleparallel
cosmological models over their other modified gravity counterparts, as the
models we examine seem to be only allowing for weak singularities that too
under non general conditions.
