Electron. J. Diff. Equ., Vol. 2009(2009), No. 106, pp. 1-10.

Strong monotonicity for analytic ordinary differential equations

Sebastian Walcher, Christian Zanders

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 1, 2009.
Math Subject Classifications: 37C65, 37C25, 92C45, 34A12.
Key Words: Monotone dynamical system; limit set; irreducible; compartmental model.

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Sebastian Walcher
Lehrstuhl A für Mathematik, RWTH Aachen
52056 Aachen, Germany
email: walcher@matha.rwth-aachen.de
Christian Zanders
Lehrstuhl A für Mathematik, RWTH Aachen
52056 Aachen, Germany
email: christian.zanders@matha.rwth-aachen.de

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