Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 44, Issue 3, Pages 1636-1673Publisher
SIAM PUBLICATIONS
DOI: 10.1137/110840509
Keywords
chemical reaction networks; mass-action; Persistence Conjecture; Global Attractor Conjecture; persistence; global stability; interaction networks; population processes; polynomial dynamical systems
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Funding
- NIH [R01GM086881]
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This paper concerns the long-term behavior of population systems, and in particular of chemical reaction systems, modeled by deterministic mass-action kinetics. We approach two important open problems in the field of chemical reaction network theory: the Persistence Conjecture and the Global Attractor Conjecture. We study the persistence of a large class of networks called lower-endotactic and, in particular, show that in weakly reversible mass-action systems with two-dimensional stoichiometric subspace all bounded trajectories are persistent. Moreover, we use these ideas to show that the Global Attractor Conjecture is true for systems with three-dimensional stoichiometric subspace.
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