Basin of Attraction through Invariant Curves and Dominant Functions
We study a second-order difference equation of the form ₙ₊₁= ₙ(ₙ₋₁) + ℎ, where both () and () 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. F...
محفوظ في:
| المؤلف الرئيسي: | |
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| مؤلفون آخرون: | , |
| التنسيق: | article |
| منشور في: |
2015
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| الوصول للمادة أونلاين: | http://hdl.handle.net/11073/16678 |
| الوسوم: |
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| الملخص: | We study a second-order difference equation of the form ₙ₊₁= ₙ(ₙ₋₁) + ℎ, where both () and () 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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