A super-predator, predator, and prey model with logistic growth

In this work, qualitative properties of a super-predator, predator, and prey model with logistic growth have been investigated. Stability analysis has been performed and eight equilibrium points have been found where two of them present possibility of Hopf bifurcation. Under given conditions the possibility for Hopf bifurcation to occur has been thoroughly analyzed by making according transformations by corresponding in variants. It has been observed that it is possible to reduce the system to two dimensions under five different conditions on parameters out of a total of sixteen cases where an algebraic invariant of the system is present. Results show that a super-predator, predator, and prey model exhibits more realistic properties among well-known similar models.