Globally dynamical behaviors for a class of nonlinear functional difference equation with almost periodic coefficients

A new approach will be used to obtained the existence and uniqueness of positive almost periodic solution x˜(n) of the following nonlinear functional difference equation:Δx(n)=-a(n)x(n)+f(n,x(n-τ(n))).Δx(n)=-a(n)x(n)+f(n,x(n-τ(n))).Also, some sufficient conditions are established for global attractivity of x˜(n) . For the proof of existence and uniqueness of x˜(n), the method used here is better than contraction mapping principle. Meanwhile, when our main results applied to some famous discrete models (Lasota–Wazewska model and Hematopoiesis model), some new statements will be obtained and these results complement existing ones.