Global Asymptotic Stability for a Fourth-Order Rational Difference Equation
DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2009 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2009
- Doi Numarası: 10.1155/2009/616982
- Dergi Adı: DISCRETE DYNAMICS IN NATURE AND SOCIETY
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
Our aim is to investigate the global behavior of the following fourth-order rational difference equation: x(n+1) = (x(n)x(n-2)x(n-3) + x(n) + x(n-2) + x(n-3) + a) / (x(n)x(n-2) + x(n)x(n-3) + x(n-2)x(n-3) + 1 + a), n = 0, 1, 2, ... where a is an element of [0,infinity) and the initial values x(-3), x(-2), x(-1), x(0) is an element of (0, infinity). To verify that the positive equilibrium point of the equation is globally asymptotically stable, we used the rule of the successive lengths of positive and negative semicycles of nontrivial solutions of the aforementioned equation. Copyright (C) 2009 M. T. Gulpinar and M. Bayram.