  This work studies relationships between monotonicity and contractivity, and
applies the results to establish that many reaction networks are weakly
contractive, and thus, under appropriate compactness conditions, globally
convergent to equilibria. Verification of these properties is achieved through
a novel algorithm that can be used to generate cones for monotone systems. The
results given here allow a unified proof of global convergence for several
classes of networks that had been previously studied in the literature.
