# American Institute of Mathematical Sciences

2006, 6(1): 97-110. doi: 10.3934/dcdsb.2006.6.97

## A global attractivity result for maps with invariant boxes

 1 Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881-0816, United States, United States

Received  April 2005 Revised  September 2005 Published  October 2005

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.
Citation: M. R. S. Kulenović, Orlando Merino. A global attractivity result for maps with invariant boxes. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 97-110. doi: 10.3934/dcdsb.2006.6.97
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