  The use of mathematical models has helped to shed light on countless
phenomena in chemistry and biology. Often, though, one finds that systems of
interest in these fields are dauntingly complex. In this paper, we attempt to
synthesize and expand upon the body of mathematical results pertaining to the
theory of multiple equilibria in chemical reaction networks (CRNs), which has
yielded surprising insights with minimal computational effort. Our central
focus is a recent, cycle-based theorem by Gheorghe Craciun and Martin Feinberg,
which is of significant interest in its own right and also serves, in a
somewhat restated form, as the basis for a number of fruitful connections among
related results.
