A global convergence result for strongly monotone systems with positive   translation invariance
  We show that strongly monotone systems of ordinary differential equations which have a certain translation-invariance property are so that all solutions converge to a unique equilibrium. The result may be seen as a dual of a well-known theorem of Mierczynski for systems that satisfy a conservation law. An application to a reaction of interest in biochemistry is provided as an illustration. 
David Angeli and Eduardo D. Sontag