Josef Hofbauer: A Unified Approach to Persistence
Acta Applicandae Mathematicae 14 (1989), 11-22
In this paper we present a simplified approach to persistence.
We show in section 1 that essentially all known persistence theorems,
including those of Butler, Freedman and Waltman [3,4], Gard and Hallam ,
Fonda , Hofbauer , Hutson  are all rather immediate consequences of a
classical result of Ura and Kimura 
on the flow near a compact invariant set, see chapter VI of Bhatia and
(This result was independently discovered by
Barnabas Garay :
Uniform persistence and chain recurrence.
J. Math. Anal. Appl. 139 (1989), 372-382.)
In section 2 we apply this to give a new and direct proof of the
geometric permanence condition for Lotka-Volterra equations, and in
section 3 we illustrate the whole
approach with a concrete two-predator two-prey system.
Download: preprint dvi (sorry, no figures)
reprint (Please note that the above abstract is missing from the published paper)