  A comparative study of the $\Lambda$ hyperon equations of state of Banik,
Hempel and Banyopadhyay (BHB) \citep{bhb} and \citet{shen11} (denoted as HShen
$\Lambda$) for core collapse supernova (CCSN) simulations is carried out in
this work. The dynamical evolution of a protoneutron star (PNS) into a black
hole is investigated in core collapse supernova simulations in the general
relativistic one dimensional code using the BHB$\Lambda \phi$ and HShen
$\Lambda$ equation of state (EoS) tables and different progenitor models from
Woosley and Heger \citep{Woos}. Radial profiles of the mass fractions of
baryons, the density as well as the temperature in the PNS at different moments
in time, are compared for both EoS tables. The behaviour of the central density
of the PNS with time is demonstrated for those two $\Lambda$ hyperon EoS tables
and compared with their corresponding nuclear EoS tables. It is observed that
the black hole formation time is higher in the BHB$\Lambda \phi$ case than in
the HShen $\Lambda$ EoS for the entire set of progenitor models adopted here,
because the repulsive $\Lambda$-$\Lambda$ interaction makes the BHB$\Lambda
\phi$ EoS stiffer. Neutrino emission with the $\Lambda$ hyperon EoS ceases
earlier than that of its nuclear counterpart. The long duration evolution of
the shock radius and gravitational mass of the PNS after a successful supernova
explosion with enhanced neutrino heating are studied with the BHB$\Lambda \phi$
EoS and $s$20WH07 progenitor model. The PNS is found to remain stable for 4 s
and might evolve into a cold neutron star.
