Kolloquium der angewandten Mathematik

In this talk, I will consider biochemical networks and address the existence of unstable equilibria based only on the network structure. In particular, I will identify minimal sources of instability, so-called unstable cores, and discuss several of their features. For example: an unstable core can be classified in autocatalytic vs nonautocatalytic, and the presence of at least one autocatalytic core characterizes autocatalysis in network. Further, unstable cores serve as predictive tools for understanding the dynamic range of a network, sufficiently determining whether a network admits multiple equilibria or periodic oscillations. The presented approach relies on bifurcation theory and multiscale methods.