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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