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http://dx.doi.org/10.14317/jami.2011.29.3_4.879

GLOBAL STABILITY OF A NONLINEAR DIFFERENCE EQUATION  

Wang, Yanqin (School of Physics & Mathematics, Changzhou University)
Publication Information
Journal of applied mathematics & informatics / v.29, no.3_4, 2011 , pp. 879-889 More about this Journal
Abstract
In this paper, we investigate the local asymptotic stability, the invariant intervals, the global attractivity of the equilibrium points, and the asymptotic behavior of the solutions of the difference equation $x_{n+1}=\frac{a+bx_nx_{n-k}}{A+Bx_n+Cx_{n-k}}$, n = 0, 1,${\ldots}$, where the parameters a, b, A, B, C and the initial conditions $x_{-k}$, ${\ldots}$, $x_{-1}$, $x_0$ are positive real numbers.
Keywords
Difference equation; Equilibrium point; Local asymptotic stability; Invariant interval; Global asymptotic stability;
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