Translation-invariant monotone systems, and a global convergence result for enzymatic futile cycles

Strongly monotone systems of ordinary differential equations which have a certain translation-invariance property are shown to have the property that all projected solutions converge to a unique equilibrium. This result may he seen as a dual of a well-known theorem of Mierczynski for systems that satisfy a conservation law. As an application, it is shown that enzymatic futile cycles have a global convergence property. (c) 2006 Elsevier Ltd. All rights reserved.