| Abstract |
Dynamical systems with polynomial right-hand sides are very important in various applications,
e.g., in biochemistry and population dynamics. The mathematical study of these dynamical
systems is challenging due to the possibility of multistability, oscillations, and chaotic dynamics.
One important tool for this study is the concept of reaction systems, which are dynamical systems
generated by reaction networks for some choices of parameter values. Among these, disguised
toric systems are remarkably stable: they have a unique attracting fixed point, and cannot
give rise to oscillations or chaotic dynamics. The computation of the set of parameter values
for which a network gives rise to disguised toric systems (i.e., the disguised toric locus of the
network) is an important but difficult task. We introduce new ideas based on network fluxes for
studying the disguised toric locus. We prove that the disguised toric locus of any network G is a
contractible manifold with boundary, and introduce an associated graph Gmax that characterizes
its interior. These theoretical tools allow us, for the first time, to compute the full disguised
toric locus for many networks of interest. |