Existence of positive periodic solutions for difference equations with feedback control

We apply the continuation theorem of coincidence degree theory to study the existence of positive periodic solutions for the following difference equations 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+ are all ω-periodic functions and m is a positive integer.