Existence of positive periodic solutions of nonlinear discrete model exhibiting the Allee effect

In this paper we shall consider the discrete nonlinear delay population model with Allee effectx(n+1)=x(n)exp(a(n)+b(n)xp(n-ω)-c(n)xq(n-ω)),where a(n), b(n) and c(n) are positive sequences of period ω and p and q are positive integers. By using the coincidence degree theorem as well as some priori estimates we will establish a sufficient condition for the existence of positive periodic solution {xn∗}.