A global attractivity criterion for nonlinear non-autonomous difference equations

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 .

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...

Stability and Global Attractivity for a Class of Nonlinear Delay Difference Equations

where c ∈ [0,1) is a given constant, k is a positive integer, f : R→ R is continuous and f (0)= 0, f (u) = 0 for u = 0. Such a equation arises from some of the earliest mathematical models of the macroeconomic “trade cycle,” and have attracted a great deal of attention (see, e.g., [1, 4, 5, 6, 7, 8, 9, 10] and references cited therein). When k = 1, Sedaghat [9] obtained some sufficient conditio...

Global Attractivity of a Family of Max-Type Difference Equations

On Global Attractivity of a Class of Nonautonomous Difference Equations

We mainly investigate the global behavior to the family of higher-order nonautonomous recursive equations given by yn p ryn−s / q φn yn−1, yn−2, . . . , yn−m yn−s , n ∈ N0, with p ≥ 0, r, q > 0, s,m ∈ N and positive initial values, and present some sufficient conditions for the parameters andmaps φn : R m → R , n ∈ N0, under which every positive solution to the equation converges to zero or a u...