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Title: Global asymptotic stability of the higher order equation x_ {n+ 1}=\ frac {ax_ {n}+ bx_ {nk}}{A+ Bx_ {nk}}
Authors: Saleh, Mohammad
Farahat, A.
Keywords: Differential equations, Nonlinear;Fluid dynamics - Mathematical models
Issue Date: 2017
Publisher: J. Appl. Math. Comput.
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.
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