The dynamics of a general nonlinear Leslie matrix model for a semelparous population is investigated. We are especially concerned with the attractivity of the single-class state, in which all but one cohort (or year-class) are missing. Our result shows that the single-class state is attractive if inter-class competition is severe. Conversely, if intra-class competition is severe, the single-class state is repelling. Numerical investigations show that all classes do not necessarily coexist even if the single-class state is repelling.
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