RESUMEN
For mass action kinetics,
the capacity for multiple equilibria
in an isothermal
homogeneous continuous flow stirred tank
reactor is determined by
the structure of the underlying
network of chemical reactions. We suggest a new graph-theoretical
method for discriminating between complex reaction networks that can admit multiple equilibria and those that cannot.
In particular, we associate
with each network a species-reaction graph, which is similar to reaction network
representations drawn by biochemists, and we show that, if
the graph satisfies certain weak conditions, the differential equations corresponding to the network
cannot admit multiple equilibria {\em no matter what
values the rate constants take}. Because these conditions are very mild, they
amount to powerful (and quite delicate) necessary conditions that a network must satisfy if it
is to have
the capacity to engender multiple equilibria. Broad qualitative results of this
kind are especially
apt, for individual reaction rate constants
are rarely known fully for complex
reaction networks (if they are known
at all). Some concluding remarks address connections to biology.