Power-Law Kinetics and Determinant Criteria for the Preclusion of Multistationarity in Networks of Interacting Species

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

We present determinant criteria for the preclusion of nondegenerate multiple steady states in networks of interacting species. A network is modeled as a system of ordinary differential equations in which the form of the species formation rate function is restricted by the reactions of the network and how the species influence each reaction. We characterize families of so-called power-law kinetics for which the associated species formation rate function is injective within each stoichiometric class and thus the network cannot exhibit multistationarity. The criterion for power-law kinetics is derived from the determinant of the Jacobian of the species formation rate function. Using this characterization, we further derive similar determinant criteria applicable to general sets of kinetics. The criteria are conceptually simple, computationally tractable, and easily implemented. Our approach embraces and extends previous work on multistationarity, such as work in relation to chemical reaction networks with dynamics defined by mass-action or noncatalytic kinetics, and also work based on graphical analysis of the interaction graph associated with the system. Further, we interpret the criteria in terms of circuits in the so-called DSR-graph.
OriginalsprogEngelsk
TidsskriftS I A M Journal on Applied Dynamical Systems
Vol/bind12
Udgave nummer4
Sider (fra-til)1685-1721
Antal sider37
ISSN1536-0040
DOI
StatusUdgivet - 16 okt. 2013

ID: 94753181