Speaker
Supriya Krishnamurti
(SU)
Description
The study of Chemical Reaction Networks (CRN's) is a very
active field. Earlier well-known results [1,2] identify a
topological quantity called deficiency, for any CRN, which,
when exactly equal to zero, leads to a factorized
steady-state for these networks. No results exist however
for the steady states of non-zero-deficiency networks. Here
we show how to write the full moment-hierarchy for any
non-zero-deficiency CRN obeying mass-action kinetics, in
terms of equations for the factorial moments (FM). Using
these, we can recursively predict values for lower moments
from higher moments, reversing the procedure usually used to
solve moment hierarchies. We show, for non-trivial examples,
that in this manner we can predict to high accuracy, any
moment of interest, for CRN's with non-zero deficiency and
non-factorizable steady states.
1. M. Feinberg, Chemical reaction network structure and the
stability of complex isothermal reactors -- I. The
deficiency zero and deficiency one theorems, Chem. Enc.
Sci., 42, 2229, (1987)
2. D. F. Anderson, G. Craciun, and T. G. Kurtz,
Product-form stationary distributions for deficiency zero
chemical reaction networks, Bull. Math. Bio., 72, 1947 (2010)
