Permanence of a single species discrete model with feedback control and delay

Sufficient conditions are obtained for the permanence of the following single species discrete model with feedback control: {N(n+1)=N(n)exp[r(n)(1−N(n−m)k(n)−c(n)μ(n))],Δμ(n)=−a(n)μ(n)+b(n)N(n−m), where a:Z→(0,1),c,k,r,b:Z→R+a:Z→(0,1),c,k,r,b:Z→R+ are all nonnegative functions and mm is a positive constant.