Dynamic behaviors of a stage-structured cooperation model

Abstract

In this paper, a two-species May type cooperation model with stage structure is presented and studied. Results on the global extinction, partial survival and global attractivity of the positive equilibrium are given, which generalize the well-known May’s result for the two species cooperation system and, moreover, they confirm the negative effect of stage structure on the persistent of populations. Conclusions in this paper suggest that for a cooperation community, stage structure and the death rate of mature species are two of the most important reason that cause global attractivity and extinction, cooperate has no influence on the persistent property of the model, and conditions which ensure the permanence of the single species are enough to ensure the global stability of the system.