Multistationarity of biochemical reaction networks as continuous systems, beyond Thomas’ condition

par Prof. S. SOLIMAN (INRIA)

mercredi 20 mars 2013, 11:00 → 12:00 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Thomas' conjecture about the necessity of a positive circuit for the multistationarity has been proved both in the discrete and continuous setting. Nevertheless it has mostly been used in the discrete case since, as we will demonstrate, it is almost always satisfied by biochemical reaction networks. In order to work around this shortcoming, we will go back to the decomposition of the Jacobian matrix determinant and notice that, for dynamical systems corresponding to biochemical reactions, certain patterns allow the statement of a stronger necessary condition. We will illustrate how that new condition rules out the cases that trivially satisfied the classical condition of Thomas on a simple example of enzymatic reaction.