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In this paper we focus on a patch occupancy 4-dimensional model of barnacle-algae-mussel interactions with external periodic seasonal forcing proposed by Benincà et al. [Proc. Natl. Acad. Sci. USA, 112 (2015), pp. 6389--6394]. In order to understand the mechanism of the species fluctuation sustained by a cyclic succession at the edge of chaos, we investigate the corresponding system without seasonal forcing. When the mussel is absent, we give a complete description of the global asymptotic behavior of the solutions. If the mussel is present, we provide an amenable sufficient and necessary condition for the uniform persistence for the 4-dimensional system. Our analytic results on the uniform persistence provide useful necessary information for the chaotic dynamics of the periodically forced system Benincà et al. [ABSTRACT FROM AUTHOR]