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http://hdl.handle.net/20.500.11889/8141
Title: | Global asymptotic stability of the higher order equation xn+1=axn+bxn-kA+Bxn-k | Authors: | Saleh, M. Farhat, A. |
Keywords: | Nonlinear difference equations;Asymptotic expansions;Global asymptotic stability;Equilibrium point;Semi-cycles | Issue Date: | 2017 | Abstract: | In this paper, we investigate the local and global stability and the period two solutions of all nonnegative solutions of the difference equation, xn+1 = axn + bxn−k A + Bxn−k where a, b, A, B are all positive real numbers, k ≥ 1 is a positive integer, and the initial conditions x−k , x−k+1, ..., x0 are nonnegative real numbers. It is shown that the zero equilibrium point is globally asymptotically stable under the condition a+b ≤ A, and the unique positive solution is also globally asymptotically stable under the condition a − b ≤ A ≤ a + b. By the end, we study the global stability of such an equation through numerically solved examples. | URI: | http://hdl.handle.net/20.500.11889/8141 |
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