Abstract
In this paper, we study the global dynamics of a class of 3-dimensional Lotka--Volterra systems with eight parameters. This system describes two predators competing for the same food; i.e., they share one prey. By theoretical analysis on this system, we obtain sufficient and necessary conditions for the principle of competitive exclusion to hold and give the global dynamical behavior of the three species in the first octant. It is shown that there are two coexistence states for the three species: periodic oscillations and steady states, which depend on the resource for the prey. These results are biologically important in pest control.
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