Delay differential equations and dynamical systems, Proc. Conf., Claremont/CA (USA) 1990, Lect. Notes Math. 1475, 31-40 (1991).
[For the entire collection see Zbl 0727.00007.]
The differential system is said to be persistent if
when . These systems describe the dynamics of interacting populations in a closed environment and the persistence implies the survival of all the components of the ecosystem. The author gives a description of the mathematical models connected with these biological situations distinguishing two approaches: the analysis of the flow on the boundary and the use of a Lyapunov-like function. In the survey there are no proofs of the theorems but many examples and updated references.