Global stability of a rational difference equation |
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Authors: | Lin-Xia Hu Wan-Tong Li |
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Institution: | aDepartment of Mathematics, Tianshui Normal University, Tianshui, Gansu 741001, People’s Republic of China bSchool of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China |
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Abstract: | In this paper, we study the global stability of the difference equation , where the parameters a,ai(0,∞) for i=0,…,k, x-k,…, x-10,∞) and x0(0,∞). We prove that the unique positive equilibrium is globally asymptotically stable if and only if it is locally asymptotically. Also we provide sufficient condition for it to be globally asymptotically stable and our results solve the open problem proposed by Kulenović and Ladas (Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures, Chapman & Hall/CRC, Boca Raton, 2002). |
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Keywords: | Difference equation Global attractor Globally asymptotically stable |
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