  In ecology, foraging requires animals to expend energy in order to obtain
resources. The cost of foraging can be reduced through kleptoparasitism, the
theft of a resource that another individual has expended effort to acquire.
Thus, kleptoparasitism is one of the most significant feeding techniques in
ecology. In this study, we investigate a two predator one prey paradigm in
which one predator acts as a kleptoparasite and the other as a host. This
research considers the post-kleptoparasitism scenario, which has received
little attention in the literature. Parametric requirements for the existence
as well as local and global stability of biologically viable equilibria have
been proposed. The occurrences of various one parametric bifurcations, such as
saddle-node bifurcation, transcritical bifurcation, and Hopf bifurcation, as
well as two parametric bifurcations, such as Bautin bifurcation, are explored
in depth. Relatively low growth rate of first predator induces a subcritical
Hopf bifurcation although a supercritical Hopf bifurcation occurs at relatively
high growth rate of first predator making coexistence of all three species
possible. Some numerical simulations have been provided for the purpose of
verifying our theoretical conclusions.
