## Abstract

We study a second-order difference equation of the form z_{n+1} = z_{n} F (z_{n-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 language | English |
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Article number | 160672 |

Journal | Discrete Dynamics in Nature and Society |

Volume | 2015 |

DOIs | |

Publication status | Published - 2015 |

## ASJC Scopus subject areas

- Modelling and Simulation