Existence of positive periodic solutions for neutral delay Gause-type predator–prey system

By using a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of positive periodic solutions for neutral delay Gause-type predator–prey system.x′(t)=x(t)[r(t)-a(t)x(t-σ(t))-b(t)x′(t-σ(t))]-ϕ(t,x(t))y(t-τ1(t)),y′(t)=y(t)[-d(t)+h(t,x(t-τ2(t)))].In addition, our results are applicable to neutral delay predator–prey systems with different types of functional responses such as Holling-type II and Ivlev-type.