Speaker
Description
Polynomial dynamical systems arise in many applications (e.g., biochemistry, population dynamics) but are hard to analyze because they can display multistability, oscillations, and chaos. Mass-action systems, and in particular complex-balanced (toric) systems, are remarkably stable: they admit a unique attracting equilibrium and rule out oscillations and chaos. We study the set of rate constants for which a mass-action system is dynamically equivalent to a complex-balanced system, the disguised toric locus, and introduce a flux-based toolkit for its analysis and computation. We prove the disguised toric locus is homeomorphic to a prism over the disguised toric flux locus, a polyhedral cone with rich combinatorial structure. This leads to new theoretical results on the geometry of the disguised toric locus: that is a contractible manifold with boundary. This prism/flux viewpoint also brings practical consequences: an explicit computational strategy that, for the first time, computes the full disguised toric locus for many networks of interest. Based on joint work with Boros, Craciun, Jin, and Henriksson (2510.03621)
