Global Asymptotic Stability for Linear Fractional Difference Equation. (1st July 2014)

• Record Type: Journal Article
• Authors: Brett, A.; Janowski, E. J.; Kulenović, M. R. S.
• Other Names: Chen Zong-Xuan Academic Editor.
• Is Part Of: Journal of difference equations. Volume 2014(2014)
• Publication Date: 2014-07-01
• Subjects: Difference equations -- Periodicals; Difference equations; Periodicals; 515.625
• DOI: 10.1155/2014/275312
• Languages: English
• ISSNs: 2356-7856

Abstract

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.