| | |
Summary: Boundedness of trajectories for weakly
reversible, single linkage class reaction systems
David F. Anderson1
June 16, 2011
Abstract
This paper is concerned with the dynamical properties of determin-
istically modeled chemical reaction systems with mass-action kinetics.
Such models are ubiquitously found in chemistry, population biology,
and the burgeoning field of systems biology. A basic question, whose
answer remains largely unknown, is the following: for which network
structures do trajectories of mass-action systems remain bounded in
time? In this paper, we conjecture that the result holds when the
reaction network is weakly reversible, and prove this conjecture in the
case when the reaction network consists of a single linkage class, or
connected component.
1 Introduction
Building off the work of Fritz Horn, Roy Jackson, and Martin Feinberg
[8, 9, 10, 12, 13, 14] the mathematical theory termed "Chemical Reaction
Network Theory" has, over the past 40 years, determined many of the ba-
sic qualitative properties of chemical reaction networks and, more generally,
|
