Mathematics Faculty Publications

Global Asymptotic Stability for Linear Fractional Difference Equation

Ann Brett, University of Rhode IslandFollow
E. J. Janowski, University of Rhode Island
Mustafa Kulenovic, University of Rhode IslandFollow

Document Type

Article

Date of Original Version

7-1-2014

Abstract

Consider the difference equation x_n₊₁ = (α + Σ^k_i=0 a_ix_n_-i)/(β + Σ^k_i₌₀ b_ix_n-i), n = 0, 1, . . ., where all parameters α, β, a_i,b_i, i = 0, 1,…., k, and the initial conditions x_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.

Citation/Publisher Attribution

A. Brett, E. J. Janowski, and M. R. S. Kulenović, “Global Asymptotic Stability for Linear Fractional Difference Equation,” Journal of Difference Equations, vol. 2014, Article ID 275312, 11 pages, 2014.

Available at: http://dx.doi.org/10.1155/2014/275312