Global attractivity in nonlinear delay 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 .

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 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...

Attractivity of Nonlinear Impulsive Delay Differential Equations

The attractivity of nonlinear differential equations with time delays and impulsive effects is discussed. We obtain some criteria to determine the attracting set and attracting basin of the impulsive delay system by developing an impulsive delay differential inequality and introducing the concept of nonlinear measure. Examples and their simulations illustrate the effectiveness of the results an...

Global Attractivity of a Family of Max-Type Difference Equations