  This paper presents a computational solution to determine if a chemical
reaction network endowed with power-law kinetics (PLK system) has the capacity
for multistationarity, i.e., whether there exist positive rate constants such
that the corresponding differential equations admit multiple positive steady
states within a stoichiometric class. The approach, which is called the
"Multistationarity Algorithm for PLK systems" (MSA), combines (i) the extension
of the "higher deficiency algorithm" of Ji and Feinberg for mass action to PLK
systems with reactant-determined interactions, and (ii) a method that
transforms any PLK system to a dynamically equivalent one with
reactant-determined interactions. Using this algorithm, we obtain two new
results: the monostationarity of a popular model of anaerobic yeast
fermentation pathway, and the multistationarity of a global carbon cycle model
with climate engineering, both in the generalized mass action format of
biochemical systems theory. We also provide examples of the broader scope of
our approach for deficiency one PLK systems in comparison to the extension of
Feinberg's "deficiency one algorithm" to such systems.
