On sharp conditions for the global stability of a difference equation satisfying the Yorke condition
Continuing our previous investigations, we give simple sufficient conditions for global stability of the zero solution of the difference equation xn+1 = qxn + fn (xn ,..., xn-k ), n ∈ Z, where nonlinear functions fn satisfy the Yorke condition. For every positive integer k, we rep...
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| Datum: | 2008 |
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| Hauptverfasser: | , , , , , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2008
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3138 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | Continuing our previous investigations, we give simple sufficient conditions for global stability
of the zero solution of the difference equation
xn+1 = qxn + fn (xn ,..., xn-k ), n ∈ Z,
where nonlinear functions fn satisfy the Yorke condition.
For every positive integer k, we represent the interval (0, 1]
as the union of [(2k + 2) /3] disjoint subintervals, and, for q from each subinterval, we present a
global-stability condition in explicit form. The conditions obtained are sharp for the class of equations satisfying the Yorke condition. |
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