Special Session 135: Dynamical Systems in Mathematical Biology: Epidemiology, Population Dynamics, and Reaction Networks

Computational approaches to inheritance of dynamics in reaction networks
Casian Pantea
West Virginia University
USA
Co-Author(s):    
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 $X$? by identifying a smaller network $\mathcal M$ with property $X$ 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.