Basin of Attraction through Invariant Curves and Dominant Functions
- Ziyad AlSharawi
- Asma Al-Ghassani
- A. M. Amleh
Publication date
January 2015
DOI Publisher
Hindawi Limited ISSN
1026-0226 Journal
Discrete Dynamics in Nature and SocietyAbstract
We study a second-order difference equation of the form zn+1=znF(zn-1)+h, where both F(z) and zF(z) are decreasing. We consider a set of invariant curves at h=1 and use it to characterize the behaviour of solutions when h>1 and when 01 is related to the Y2K problem. For 0<h<1, we study the stability of the equilibrium solutions and find an invariant region where solutions are attracted to the stable equilibrium. In particular, for certain range of the parameters, a subset of the basin of attraction of the stable equilibrium is achieved by bounding positive solutions using the iteration of dominant functions with attracting equilibria
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