The Dynamics of Weakly Reversible Population Processes near Facets

11 years 3 months ago
The Dynamics of Weakly Reversible Population Processes near Facets
This paper concerns the dynamical behavior of weakly reversible, deterministically modeled population processes near the facets (codimension-one faces) of their invariant manifolds and proves that the facets of such systems are “repelling.” It has been conjectured that any population process whose network graph is weakly reversible (has strongly connected components) is persistent. We prove this conjecture to be true for the subclass of weakly reversible systems for which only facets of the invariant manifold are associated with semilocking sets, or siphons. An important application of this work pertains to chemical reaction systems that are complex-balancing. For these systems it is known that within the interior of each invariant manifold there is a unique equilibrium. The global attractor conjecture states that each of these equilibria is globally asymptotically stable relative to the interior of the invariant manifold in which it lies. Our results pertaining to weakly reversibl...
David F. Anderson, Anne Shiu
Added 30 Jan 2011
Updated 30 Jan 2011
Type Journal
Year 2010
Authors David F. Anderson, Anne Shiu
Comments (0)