期刊
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
卷 12, 期 4, 页码 1685-1721出版社
SIAM PUBLICATIONS
DOI: 10.1137/120873388
关键词
influence specification; reaction network; monotone kinetics; Jacobian; degenerate; power-law
资金
- Lundbeck Foundation, Denmark
- Danish Research Councils
- Leverhulme Trust, UK
- Generalitat de Catalunya
- Ministerio de Economia y Competitividad of the Spanish government [MTM2012-38122-C03-01]
- Lundbeck Foundation [R49-2010-5841] Funding Source: researchfish
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.
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