Global attractivity in a rational delay difference equation with quadratic terms

Abstract

For the following rational difference equation with arbitrary delay and quadratic terms:

we determine sufficient conditions on the parameter values which guarantee that the unique non-negative fixed point attracts all positive solutions. When the fixed point is the origin (F = 0), we show that it attracts all non-negative solutions of the more general equation

where . We also show that altering some of the above conditions on parameters causes the origin to not be globally attracting.

Keywords:

• rational
• delay
• quadratic terms
• global stability

2000 Mathematics Subject Classification::

• 39A10
• 39A11