Mathematics – Dynamical Systems
Scientific paper
2012-02-16
Mathematics
Dynamical Systems
Scientific paper
We present a unified framework for the preclusion of non-degenerate multiple steady states in a network of interacting species. Interaction networks are modeled via systems of ordinary differential equations in which the form of the species rate function is restricted by the reactions of the network and how the species influence each reaction. We characterize the set of interaction networks for which any choice of associated rate function is injective within each stoichiometric class and thus cannot exhibit multistationarity. Our criteria rely on the determinant of the Jacobian of the species rate functions that belong to the class of so-called general mass-action kinetics. The criteria are computationally tractable and easily implemented. Our approach embraces and extends much previous work on multistationarity, such as work in relation to chemical reaction networks with dynamics defined by mass-action or non-catalytic kinetics, and also work based on the graphical analysis of the interaction graph associated to the system.
Feliu Elisenda
Wiuf Carsten
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