English
Français
Log In
Email address
Password
Log in
New user? Click here to register.
Have you forgotten your password?
Research Outputs
Researchers
Disciplines
English
Français
Log In
Email address
Password
Log in
New user? Click here to register.
Have you forgotten your password?
Home
Research Output
Articles
Basin of Attraction through Invariant Curves and Dominant Functions
Details
Options
Export
Basin of Attraction through Invariant Curves and Dominant Functions
Journal
Discrete Dynamics in Nature and Society
Date Issued
2015
Author(s)
Alsharawi, Z.
Al-Ghassani, A.
Amleh, A. M.
DOI
10.1155/2015/160672
URI
http://hdl.handle.net/20.500.12458/33
Abstract
We study a second-order difference equation of the form z<inf>n+1</inf> = z<inf>n</inf> F (z<inf>n-1</inf>) + 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. © 2015 Ziyad AlSharawi et al.
File(s)
Amleh, Amal, Alsharawi, Al-Ghassani - 2015 - Basin of Attraction through Invariant Curves and Dominant Functions-annotated.pdf (2.09 MB)
Scopus© citations
0
Acquisition Date
Jul 5, 2022
Views
61
Last Month
4
Acquisition Date
Jul 5, 2022
Downloads
2
Acquisition Date
Jul 5, 2022
google-scholar
Check