Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 106, pp. 1-10.

Title: Strong monotonicity for analytic
       ordinary differential equations 

Authors: Sebastian Walcher (RWTH Aachen, Germany)
         Christian Zanders (RWTH Aachen, Germany)

Abstract:
 We present a necessary and sufficient criterion for the flow
 of an analytic ordinary differential equation to be strongly
 monotone; equivalently, strongly order-preserving.
 The criterion is given in terms of the reducibility set
 of the derivative of the right-hand side. Some applications
 to systems relevant in biology and ecology, including nonlinear
 compartmental systems, are discussed.
 
Submitted August 21, 2009. Published September 01, 2009.
Math Subject Classifications: 37C65, 37C25, 92C45, 34A12.
Key Words: Monotone dynamical system; limit set; irreducible;
           compartmental model.