Minimal invariant regions and minimal globally attracting regions for variable-k reaction systems. (English) Zbl 1510.37127
The authors consider reaction network models in the form of ordinary differential equations with powers on the right-hand side. The network is described by a graph with weights (which are reaction rate constants). The authors give an explicit construction of the minimal invariant regions and minimal globally attracting regions for variable-\(k\) dynamical systems generated by two reversible reactions. Their aim is to prove persistence and permanence, i.e., positiveness of all concentrations and staying of the state in a neighbourhood of a point. The understanding of these properties is important both in ecological models and in chemical dynamics.
Reviewer: Ilya A. Chernov (Petrozavodsk)
MSC:
| 37N25 | Dynamical systems in biology |
| 37E25 | Dynamical systems involving maps of trees and graphs |
| 37C75 | Stability theory for smooth dynamical systems |
| 80A30 | Chemical kinetics in thermodynamics and heat transfer |
| 92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |
| 92E20 | Classical flows, reactions, etc. in chemistry |
| 92D40 | Ecology |
| 14M25 | Toric varieties, Newton polyhedra, Okounkov bodies |
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