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(n+1) = x(n)f(x(n-k), n = 0, 1, 2, ..., are attracted to the positive equilibrium of the equation. Our result applies, for example, to the delay logistic model N(t+1) = alpha-N(t)/(1 + beta-N(t-k)) and to the delay difference equation x(n+1) = x(n)e(r)(1-x)(n-k)).