Positive equilibria of reaction network models

11 Jul 2018, 15:00
New Law School/--101 (University of Sydney)

New Law School/--101

University of Sydney



Positive equilibria of reaction network models

  • Maya Mincheva ()


Multistationarity, or the existence of several positive equilibria, is a common property of biochemical reaction networks' models. The existence of multistationarity can be guaranteed using different approaches. In one of the talks, we explain how degree theory can be used to obtain sufficient conditions for multistationarity. Moreover, using this approach multistationarity regions in parameter space can be computed. In another talk, multistationarity of reaction networks will be characterized in terms of a rational parametrization of the equilibrium solutions. The other two talks concern a generalization of mass action kinetics systems to systems with power law kinetics, where the kinetic orders are real numbers. In one of the talks, an extension of the Deficiency Zero Theorem, which is applicable to systems with power law kinetics, will be presented. In the other talk, the existence of positive equilibria for a special class of systems with power law kinetics will be discussed. Applications to signalling networks will be presented in all of the talks.

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