Weak Dynamical Nonemptiability and Persistence of Chemical Kinetics Systems

Source abstract

A frequently desirable characteristic of chemical kinetics systems is that of persistence, the property that if all the species are initially present, then none of them may tend toward extinction. It is known that solutions of deterministically modeled mass-action systems may approach only portions of the boundary of the positive orthant which correspond to semilocking sets (alternatively called siphons). Consequently, most recent work on persistence of these systems has been focused on these sets. In this paper, we focus on a result which states that, for a conservative mass-action system, persistence holds if every critical semilocking set is dynamically nonemptiable and the system contains no nested locking sets. We will generalize this result by introducing the notion of a weakly dynamically nonemptiable semilocking set and making novel use of the well-known Farkas' lemma. We will also connect this result to known results regarding complex balanced systems and systems with facets.