The effect of the remains of the carcass in a two-prey, one-predator model

We propose a two-prey, one-predator model involving the effect of the carcass. We consider a commensal interaction that a prey species eats the remains of the other prey species' carcass given by their predator. Under some biological assumptions, we construct two ODE models. We analyze the linear stability and prove the permanence of the two models. We also show that the effect of the remains of the carcass leads to chaotic dynamics for biologically reasonable choices of parameters by numerical simulations. Finally, we discuss the dynamical results and the coexistent regions of the three species.