Name
Abstract | ||
|---|---|---|
The persistence conjecture is a long-standing open problem in chemical reaction network theory. It concerns the behavior of solutions to coupled ODE systems that arise from applying mass-action kinetics to a network of chemical reactions. The idea is that if all reactions are reversible in a weak sense, then no species can go extinct. A notion that has been found useful in thinking about persistence is that of "critical siphon." We explore the combinatorics of critical siphons, with a view toward the persistence conjecture. We introduce the notions of "drainable" and "self-replicable" (or autocatalytic) siphons. We show that: Every minimal critical siphon is either drainable or self-replicable; reaction networks without drainable siphons are persistent; and nonautocatalytic weakly reversible networks are persistent. Our results clarify that the difficulties in proving the persistence conjecture are essentially due to competition between drainable and self-replicable siphons. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1007/s11538-014-0024-x | Bulletin of mathematical biology |
Keywords | Field | DocType |
Critical siphons, Persistence, Reaction network, Autocatalysis, Petri net | Discrete mathematics,Open problem,Chemical reaction network theory,Conjecture,Mathematics,Ode,Autocatalysis | Journal |
Volume | Issue | ISSN |
76 | 10 | 1522-9602 |
Citations | PageRank | References |
0 | 0.34 | 12 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Abhishek Deshpande | 1 | 0 | 0.34 |
| Manoj Gopalkrishnan | 2 | 14 | 4.56 |