The dynamics of a cooperative difference system with coefficient a Metzler matrix

Abstract

The basin of attraction to the origin in the space is obtained for the m dimensional system of difference equations of the form

when coefficient is a Metzler matrix. Some information about the dynamics of the solutions outside of the basin is also given.

Keywords::

• difference equation
• cooperative system
• M-matrix
• basin of attraction attractivity
• convergence

2000 Mathematics Subject Classification::

• Primary 39A30
• Secondary 92D25

Acknowledgements

The author would like to thank the anonymous referees for their very detailed list of useful suggestions on the first version of this manuscript.

Notes

^1. The figures were produced by using Graphing Calculator, Pacific Tech. 3.5. We got an approximation up to , since the other appeared terms are of higher order, thus the final configuration does not change much.