Global Asymptotic Stability for Linear Fractional Difference Equation. (1st July 2014) - Brett, A.; Janowski, E. J.; Kulenović, M. R. S.
Abstract : Consider the difference equationx n + 1 = ( α + ∑ i = 0 k a i x n - i ) / ( β + ∑ i = 0 k b i x n - i ),   n = 0, 1, …, where all parametersα, β, a i, b i,   i = 0, 1, …, k, and the initial conditionsx i,   i ∈ { - k, …, 0 } are nonnegative real numbers. We investigate the asymptotic behavior of the solutions of the considered equation. We give easy-to-check conditions for the global stability and global asymptotic stability of the zero or positive equilibrium of this equation.