An exploitation-competition system with negative effect of prey on its predator

This paper considers an exploitation-competition system in which exploitation is the dominant interaction when the prey is at low density, while competition is dominant when the prey is at high density due to its negative effect on the predator. The two-species system is characterized by differential equations, which are the combination of Lotka-Volterra competitive and predator-prey models. Global dynamics of the model demonstrate some basic properties of exploitation-competition systems: (i) When the growth rate of prey is extremely small, the prey cannot promote the growth of predator. (ii) When the growth rate is small, an obligate predator can survive by preying on the prey, while a facultative predator can approach a high density by the predation. (iii) When the growth rate is intermediate, the predator can approach the maximal density by an intermediate predation. (iv) When the growth rate is large, the predator can persist only if it has a large density and its predation on the prey is big. (v) Intermediate predation is beneficial to the predator under certain parameter range, while over- or under-predation is not good. Extremely big/small predation would lead to extinction of species. Numerical simulations confirm and extend our results.