Basin of Attraction through Invariant Curves and Dominant Functions

Ziyad Alsharawi, Asma Al-Ghassani, A. M. Amleh

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Abstract

We study a second-order difference equation of the form zn+1 = zn F (zn-1) + h, where both F (z) and z F (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 0 <h <1. The case h > 1 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.

Original languageEnglish
Article number160672
JournalDiscrete Dynamics in Nature and Society
Volume2015
DOIs
Publication statusPublished - 2015

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ASJC Scopus subject areas

  • Modelling and Simulation

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