Oscillation and global attractivity in a discrete model of Nicholson's blowflies

Abstract

The delay difference equation

is a discrete analogue of the delay differential equation

which has been used in describing the dynamics of Nicholson's blowflies. See [1], [4] and [5]. We obtain sufficient conditions for the oscillation of all positive solutions of Eq. (1) about its positive equilibrium N^*. We also obtain sufficient conditions for all positive solutions of Eq. (1) to be attracted to N^*.

Keywords:

• Oscillation
• global attractivity
• Nicholson's blowflies

AMS(MOS)::

• 39A12
• 92A15

^†On leave from the Department of Mathematics, Faculty of Electrical Engineering, University of Belgrade, 11000 Belgrade, Yugoslavia.

^†On leave from the Department of Mathematics, Faculty of Electrical Engineering, University of Belgrade, 11000 Belgrade, Yugoslavia.

Notes

^†On leave from the Department of Mathematics, Faculty of Electrical Engineering, University of Belgrade, 11000 Belgrade, Yugoslavia.