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In this paper, we study the following Lotka–Volterra commensal symbiosis model of two populations with Michaelis–Menten type harvesting for the first species:  dxdt=r1x(1−xK1+αyK1)−qExm1E+m2x,dydt=r2y(1−yK2),$$ \begin{gathered} \frac{dx}{dt} = r_{1}x \biggl(1- \frac{x}{K_{1}}+\alpha \frac{y}{K_{1}} \biggr)- \frac{qEx}{m_{1}E+m_{2}x}, \\ \frac{dy}{dt} = r_{2}y \biggl(1- \frac{y}{K_{2}} \biggr), \end{gathered} $$ where r1$r_{1}$, r2$r_{2}$, K1$K_{1}$, K2$K_{2}$, α, q, E, m1$m_{1}$ and m2$m_{2}$ are all positive constants. The local and global dynamic behaviors of the system are investigated, respectively. For the limited harvesting case (i.e., q is small enough), we show that the system admits a unique globally stable positive equilibrium. For the over harvesting case, if the cooperate intensity of the both species (α) and the capacity of the second species (K2$K_{2}$) are large enough, the two species could coexist in a stable state; otherwise, the first species will be driven to extinction. Numeric simulations are carried out to show the feasibility of the main results.

The influence of commensalism on a Lotka–Volterra commensal symbiosis model with Michaelis–Menten type harvesting