| Abstract: |
| Recent work by Banaji and collaborators shows that certain enlargements of reaction networks --through the addition of species and reactions-- preserve key dynamical properties such as multistationarity, oscillations, and bifurcations. This framework enables the use of certificates for specific behaviors (e.g., a supercritical Hopf bifurcation) by reducing analysis to smaller, more tractable subnetworks. In principle, this allows one to answer the question ``Does a network {\mathcal N} exhibit dynamical property {\em X}? by identifying a smaller network {\mathcal M} with property {\em X} and a sequence of enlargements from {\mathcal M} to {\mathcal N}.
In this talk, we investigate algorithms for tackling this combinatorially explosive problem and present real-world applications of inherited Hopf bifurcation in large enzymatic networks. |
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