## DIMACS TR: 2004-15

##
A tutorial on monotone systems- with an application to chemical reaction networks

### Authors: P. De Leenheer, D. Angeli and E.D. Sontag

**
ABSTRACT
**
Monotone systems are dynamical systems for which the flow preserves a
partial order. Some applications will be briefly reviewed in this paper.
Much of the appeal of the class of monotone systems stems from the
fact that roughly, most solutions converge to the set of equilibria.
However, this usually requires a stronger monotonicity property which
is not always satisfied or easy to check in applications.
Following a result by J.F. Jiang, we show that monotonicity is enough to
conclude global attractivity if there is a unique equilibrium and if the state space
satisfies a particular condition. The proof given here is self-contained
and does not require the use of any of the results from the theory of monotone
systems. We will illustrate it on a class of chemical
reaction networks with monotone, but otherwise arbitrary, reaction
kinetics.

Paper Available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2004/2004-15.ps.gz

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