Periodic solutions in a delayed predator–prey model with nonmonotonic functional response

By using the continuation theorem of coincidence degree theory and some functional analysis techniques, several existence criteria are established for positive periodic solutions of a delayed predator–prey model with nonmonotonic functional response of the form {x′(t)=x(t)(a(t)−b(t)x(t))−g(x(t))y(t),y′(t)=y(t)(μ(t)g(x(t−τ))−d(t)), where a(t),b(t),μ(t)a(t),b(t),μ(t) and d(t)d(t) are all positive periodic continuous functions with period ω>0ω>0, ττ is a nonnegative constant and gg is a nonmonotonic functional response function. And an example is given to illustrate our main result.