On classes of reaction networks and their associated polynomial dynamical systems

• Published in: Journal of mathematical chemistry Vol. 58; no. 9; pp. 1895 - 1925
• Main Authors: Anderson, David F., Brunner, James D., Craciun, Gheorghe, Johnston, Matthew D.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.10.2020; Springer Nature B.V
• Subjects: Chemistry; Chemistry and Materials Science; Dynamical systems; Inclusions; Math. Applications in Chemistry; Networks; Original Paper; Physical Chemistry; Polynomials; Theoretical and Computational Chemistry; 92C45; 92C42; Reaction networks; 37N25; Polynomial dynamical systems; 34C20; 80A30
• ISSN: 0259-9791; 1572-8897
• DOI: 10.1007/s10910-020-01148-9

In the study of reaction networks and the polynomial dynamical systems that they generate, special classes of networks with important properties have been identified. These include reversible , weakly reversible , and, more recently, endotactic networks. While some inclusions between these network types are clear, such as the fact that all reversible networks are weakly reversible, other relationships are more complicated. Adding to this complexity is the possibility that inclusions be at the level of the dynamical systems generated by the networks rather than at the level of the networks themselves. We completely characterize the inclusions between reversible, weakly reversible, endotactic, and strongly endotactic network, as well as other less well studied network types. In particular, we show that every strongly endotactic network in two dimensions can be generated by an extremally weakly reversible network. We also introduce a new class of source-only networks, which is a computationally convenient property for networks to have, and show how this class relates to the above mentioned network types.