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Title: On the dynamics of a rational difference equation xn+1=α+βxn+γxn−kBxn+Cxn−k
Authors: Saleh, Mohammad
Alkoumi N., Farhat A.
Keywords: Stability;Nonlinear systems;Dynamical Systems
Issue Date: Jan-2017
Publisher: Chaos, Solitons and Fractals
Abstract: In this paper, we will investigate the dynamics of a nonlinear rational difference equation of a higher order. Our concentration is on invariant intervals, periodic character, the character of semi-cycles and global asymptotic stability of all positive solutions of x n +1 = α+ βx n + γx n −k Bx n + Cx n −k , n = 0 , 1 , . . . It is worth to mention that our results solve partially some of the open problems proposed by Kulenvic and Ladas in their monographs [17], [18].
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