Global stability and bifurcation analysis of a predator-prey model involving Allee effect and Monod-Haldane functional response

Source abstract

In this paper, the complexity of the dynamic behavior of the interaction between prey and predator is studied. The predator-prey relationship involves Allee effects and Monod-Haldane functional response. The constructed model has been shown to have validity in several respects, including the existence and uniqueness of the solution, as well as its non-negativity and boundedness. Three equilibrium points, namely trivial, axial, and coexistence points, are found, including their global dynamics using the Lyapunov function together with the LaSalle's invariance principle. The effect of the predation conversion rate causes changes in the dynamic behavior of predators and prey, which is characterized by the occurrence of backward bifurcation phenomena. Meanwhile, the influence of the severity of the Allee effect encourages the occurrence of the Hopf bifurcation phenomenon. In addition, the severity of the Allee effect, which is getting stronger, encourages the emergence of bistability and tristability phenomena, which cause the existence of all populations to depend on the initial conditions. The emergence of this interesting phenomenon is strengthened by providing numerical simulations consisting of bifurcation diagrams and their phase portraits, both locally and globally.