Minimal invariant regions and minimal globally attracting regions for variable-k reaction systems (Q2099184)

The authors consider reaction network models in the form of ordinary differential equations with powers in 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 proving 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.