A global attractivity result for maps with invariant boxes
By Mustafa R. S. Kulenovic, O. Merino. 2005
80 citations recorded by the source corpus.
We present a global attractivity result for maps generated by systems of autonomous difference equations. It is assumed that the map of the system leaves invariant a box, is monotone in a coordinate-wise sense (but not necessarily monotone with respect to a standard cone), and satisfies certain algebraic condition. It is shown that there exists a unique equilibrium, and that it is a global attractor. As an application, it is shown that a discretized version of the Lotka-Volterra system of differential equations of order $k$ has a global attractor in the positive orthant for certain range of parameters.
Subfields: Computer Networks and Communications, Geometry and Topology, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/bdb5ad5551f43331e2881afaa12ae7d9b54504c8
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In Computer Networks and Communications
In Geometry and Topology
In Public Health, Environmental and Occupational Health
Citations in the corpus
- Global stability for mixed monotone systems (2008, methodology): “A result of Kulenović and Merino We show that the main result of Kulenović and Merino [7] follows from Theorem 2.”