A global attractivity result for maps with invariant boxes

M. R. S. Kulenović; Orlando Merino

doi:10.3934/dcdsb.2006.6.97

Article Contents

2006, Volume 6, Issue 1: 97-110. Doi: 10.3934/dcdsb.2006.6.97

This issue Previous Article Mathematical analysis of an age-structured SIR epidemic model with vertical transmission Next Article On a well-posed turbulence model

A global attractivity result for maps with invariant boxes

M. R. S. Kulenović^1, and
Orlando Merino^1,

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

Received: March 31, 2005

Revised: August 31, 2005

Published: December 2005

Abstract Related Papers Cited by

Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 37B25; Secondary: 39A11, 39A20.

Citation:

Article Metrics

HTML views() PDF downloads(162) Cited by(0)

A global attractivity result for maps with invariant boxes

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

A global attractivity result for maps with invariant boxes

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content