Abstract
In this paper, we complete the classification on global topological structures of the three-dimensional cooperative Lotka-Volterra system with the identical intrinsic growth rate inside the Poincaré compactification of the positive octant of R3. Precisely, with the help of the replicator equations it is proved that this kind of system can have exactly 8 topologically different phase portraits. As a consequence, we obtain the necessary and sufficient conditions for the system to be bounded in the positive octant.
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