Basin of Attraction through Invariant Curves and Dominant Functions
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 0<h<1. The case h>1 is related to the Y2K problem. For...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/160672 |
| Summary: | 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 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. |
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| ISSN: | 1026-0226 1607-887X |