Multiple Equilibria in Complex Chemical Reaction Networks: I. The Injectivity Property

By Gheorghe Craciun, Martin Feinberg. SIAM Journal on Applied Mathematics, 2005

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Toric Differential Inclusions and a Proof of the Global Attractor Conjecture (2015, background): “There is great interest in understanding the persistence and global stability properties of such dynamical systems [14, 15, 9, 10, 12, 11, 19, 20, 26, 21, 22, 23, 6, 8, 2, 18, 3, 5, 17, 1, 7, 16].”
Mathematical Analysis of Chemical Reaction Systems (2018, methodology): “This property was introduced in [19], where the Jacobian criterion was shown to be a sufficient condition for injectivity, which, in turn, implies uniqueness of steady states for “open” mass-action systems, i.”
Stochastic switching in biology: from genotype to phenotype (2017, methodology): “For example, in the case of deterministic models, mathematical analysis has been used to investigate conditions for the existence of multiple equilibria [67, 68], as well as dynamical properties such as persistence and global stability [6, 12]; persistence is the condition that if all chemical speci”
Linear conjugacy of chemical reaction networks (2011, background): “Active theoretical topics within the mathematical literature include determining network conditions which guarantee locally stable dynamics [14,18,19,26,27,32], conditions which prohibit/permit multistability [7,8,11,24], and conditions which ensure the persistence of the chemical species [1, 2, 6, ”