Persistence in Dynamics and Biology

1:00 PM-3:00 PM

*Plumeria & Tiare (Salon 9 & 10)*

Persistence is an idea that came out of theoretical population biology in the 70's and 80's. In a dynamical system representing the interaction of species, the long term dynamics may be hard to determine but one would at least like to decide whether all (or some subset of ) species ultimately survive (or "persist"-hence the term persistence). More generally, and of interest in many applications outside biology, one has a dynamical system (discrete or continuous) on a metric space *X* which is the disjoint union of an open positively invariant set *Y* and a "bad" set *Z* ( e.g. representing extinction of one or more species). One wants to show that orbits starting in Y have limit sets bounded away from the bad set *Z* with the bound being uniform with respect to initial data in *Y*. In other words, *Z* is a repeller. Many sufficient conditions for persistence exist in the literature for discrete-time and continuous-time, finite and infinite-dimensional, dynamical systems. Current research in the area focuses on determining whether persistence is robust under perturbation of the underlying dynamics and on establishing persistence.

**1:00-1:25 Robust Persistence***Hal L. Smith*, Organizer; Morris W. Hirsch, University of California, Berkeley, USA; and Xiao-Qiang Zhao, Memorial University of Newfoundland, Canada**1:30-1:55 The Chemostat with an Inhibitor**- S. B. Hsu, National Tsing Hua University, Taiwan; and
*Paul Waltman*, Emory University, USA **2:00-2:25 Robust Permanence for Vector Fields**- Sebastian Schreiber, Western Washington University, USA
**2:30-2:25 Uniform Persistence in Processes with Application to Nonautonomous Competitive Models**- Xiao-Qiang Zhao, Memorial University of Newfoundland, St. John's, Canada

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Created 4/20/00; Updated 7/11/00