Speaker
Description
Cycling reaction networks are ubiquitous in nature,
underpinning key processes such as the Krebs and Kelvin
cycles. In this talk, we analyze the robustness of such networks.
Under the regularity assumption—that all supplied species are
subject to degradation—we show that the dynamics converge to
a consensus state, where all external and internal flows equalize
while species concentrations remain bounded. Our proof relies
on a suitably constructed piecewise–linear Lyapunov function
in the reaction rates. The non-regular case is substantially more
delicate, since concentrations of external species may diverge.
We show that all internal reaction rates still converge to a consensus
value. If the concentration of the minimal-input node remains bounded,
the consensus value coincides with the minimal input. Otherwise,
the rates converge to a common value that does not exceed it
