Delay differential model of one-predator two-prey system with Monod-Haldane and holling type II functional responses

In this paper, we study the dynamics of a delay differential model of predator-prey system involving teams of two-prey and one-predator, with Monod-Haldane and Holling type II functional responses, and a cooperation between the two-teams of preys against predation. We assume that the preys grow logistically and the rate of change of the predator relies on the growth, death and intra-species competition for the predators. Two discrete time-delays are incorporated to justify the reaction time of predator with each prey. The permanence of such system is proved. Local and global stabilities of interior steady states are discussed. Hopf bifurcation analysis in terms of time-delay parameters is investigated, and threshold parameters τ₁^* and τ₂^* are obtained. Sensitivity analysis that measures the impact of small changes in the model parameters into the model predictions is also investigated. Some numerical simulations are provided to show the effectiveness of the theoretical results.