Al-Sharawi, ZiyadAl-Ghassani, AsmaAmleh, Amal2020-06-042020-06-042015Basin of Attraction through Invariant Curves and Dominant FunctionsAlSharawi, Z., Al-Ghassani, A., and Amleh, A. M. (2015). Basin of attraction through invariant curves and dominant functions. Discrete Dynamics in Nature and Society, 2015. doi: 10.1155/2015/1606721607-887Xhttp://hdl.handle.net/11073/16678We 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.en-USPeer-Reviewed10.1155/2015/160672