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In this paper we simulate numerically different types of positive solutions of diffusive Lotka-Volterra competition systems: semitrivial positive solutions, semitrivial positive metasolutions, coexistence states and meta-coexistence states, in the case in which one of the species has two refuges. The existence of these solutions has been demonstrated in López-Gómez (2003). Once the location and extension of both refuges and the distribution of the resources in the territory are known, the competition strategies of each of the species can be designed and incorporated into the model. Or vice versa, if the competition strategies are known, the resources into the territory can be distributed in a way to obtain better results.