| Competition among several species is modeled using a discrete Kolmogorov model. Sufficient and sometimes necessary conditions are found for the model to exhibit various asymptotic dynamics, including persistence, extinction, and weak extinction. In situations in which some species are going extinct, these results are extended. The conditions for persistence and extinction can be applied to the species in the submodel in which the species going extinct are removed. This allows one to find additional species that go extinct or persist in the full model, although these species do not satisfy our conditions in the full model. |
