Competition and coexistence of a stochastic Holling II n-predator one-prey model

In this paper, we discuss a stochastic Holling II predator–prey model with n-predator competing for one prey. The existence of a positive solution is established by using the comparison theorem. We get the stochastic break-even concentration ${\tilde{R}}_i$ of each predator which determines the competition outcomes. When the noise intensity of the prey is small, the predator with the lowest stochastic break-even concentration will survive and other predators will go extinct. When the noise intensity of the prey is large enough, all species go to extinction. Moreover, if two predators have the same lowest stochastic break-even concentration in some conditions, the two predators can coexist. Finally, numerical simulations to illustrate the analytical results are given.

Highlights:

The article studies the dynamics of a stochastic predator–prey system with Holling II functional response and n-predator.

The sufficient conditions for the competitive exclusion and coexistence are established.

The results show that noises can affect the competition.