Multistationarity and Robustness in Reaction Networks

UBC Science Early Career Invited Lecture

In biochemical reactions, the interaction between species is represented by directed graphs and their dynamics over time is modelled with ordinary differential equations. In this talk I will discuss recent results on two key dynamical properties of steady states of chemical reaction networks: multistationarity and robustness. The ODEs are often parametric polynomials, the problem of multistationarity is essentially exploring the space of parameters for which the polynomial system has multiple positive real solutions. Moreover, the system is robust for a certain chemical species if all equilibrium points have the same concentration for that species. In other words, robustness implies that steady states lie on a hyperplane parallel to a certain coordinate plane.

This talk is based on multiple joint works with Elisenda Feliu, Badal Joshi, Tung Nguyen, Anne Shiu, Timo de Wolff, and Oguzhan Yürük.