A two-predator one-prey model of population dynamics influenced by herd behaviour of the prey

We construct a mathematical model considering the populations of multiple predators and one prey, with herd defense by the prey modelled by modifying the law of mass action with a single parameter. This modification introduces a novel bifurcation in the case where all the predators are specialists. When some predators may be generalists, the analysis is more complicated and we consider only the case of two predators of which one or two may be generalists. In this case, novel steady states occur via saddlenode bifurcation, and in some cases the coexistence steady state exhibits Hopf bifurcation to a stable limit cycle. We show that the phenomenon of finite time extinction of prey also occurs in this context. Finally, we extend the analysis from constant herding effect to a model where predator pressure increases the strength of herding.