Abstract:

Despite recent developments, describing the set of parameters that enable multistationarity in a reaction network is a challenging problem. Under certain assumptions on the network, one can associate a critical polynomial to the network that gives information about multistationarity. Especially, if the preimage of the negative real line under the critical polynomial is connected then the parameter region of multistationarity is connected. In the first part of the talk, I will present several new sufficient conditions on the critical polynomial that imply connectivity. I will give several examples of reaction networks where our algorithm can be applied. In particular, we show that the parameter region of multistationarity of the sequential and distributive phosphorylation cycle with up to seven binding sites is connected. In the second part, I will discuss a reaction network whose parameter region of multistationarity is not connected.

For zoom link (available shortly ahead of the talk) please see Seminar on the Mathematics of Reaction Networks: