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In ecology, foraging requires animals to expend energy in order to obtainresources. The cost of foraging can be reduced through kleptoparasitism, thetheft of a resource that another individual has expended effort to acquire.Thus, kleptoparasitism is one of the most significant feeding techniques inecology. In this study, we investigate a two predator one prey paradigm inwhich one predator acts as a kleptoparasite and the other as a host. Thisresearch considers the post-kleptoparasitism scenario, which has receivedlittle attention in the literature. Parametric requirements for the existenceas well as local and global stability of biologically viable equilibria havebeen proposed. The occurrences of various one parametric bifurcations, such assaddle-node bifurcation, transcritical bifurcation, and Hopf bifurcation, aswell as two parametric bifurcations, such as Bautin bifurcation, are exploredin depth. Relatively low growth rate of first predator induces a subcriticalHopf bifurcation although a supercritical Hopf bifurcation occurs at relativelyhigh growth rate of first predator making coexistence of all three speciespossible. Some numerical simulations have been provided for the purpose ofverifying our theoretical conclusions.

Two predators one prey model that integrates the effect of supplementary  food resources due to one predator's kleptoparasitism under the possibility  of retribution by the other predator