Global Attractivity of the Equilibrium of a Nonlinear Difference Equation

Global Attractivity in a Nonlinear Difference Equation

In this paper, we study the asymptotic behavior of positive solutions of the nonlinear difference equation xn+1 = xnf(xn−k), where f : [0,∞)→ (0,∞) is a unimodal function, and k is a nonnegative integer. Sufficient conditions for the positive equilibrium to be a global attractor of all positive solutions are established. Our results can be applied to to some difference equations derived from ma...

Global attractivity of a higher-order nonlinear difference equation

In this paper, we investigate the global attractivity of negative solutions of the nonlinear difference equation xn+1 = 1− xn−k A + xn , n = 0, 1, . . . , where A ∈ (−∞, 0), k is a positive integer and initial conditions x−k, · · · , x0 are arbitrary real numbers. We show that the unique negative equilibrium of abovementioned equation is a global attractor with a basin under certain conditions....

The Global Attractivity of a Higher Order Rational Difference Equation

This paper studies global asymptotic stability for positive solutions to the equation yn = yn−kyn−lyn−m + yn−k + yn−l + yn−m 1 + yn−kyn−l + yn−kyn−m + yn−lyn−m , n = 0, 1, . . . , with y−m, y−m+1, . . . , y−1 ∈ (0,∞) and 1 ≤ k < l < m. The paper also includes a listing of possible semi-cycle structures for various (k, l, m). The results generalize several others in the recent literature.

On the Global Attractivity of a Max-Type Difference Equation

Global Attractivity in Nonlinear Delay Difference Equations

We obtain a set of sufficient conditions under which all positive solutions of the nonlinear delay difference equation x„+l = x„f(xn_k), n = 0,1,2,..., are attracted to the positive equilibrium of the equation. Our result applies, for example, to the delay logistic model JVI+i = aN¡/(\ +ßNt_k) and to the delay difference equation xn+i = x„er^~x"-k'1 .