Positive periodic solutions for a class of 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−σ1)−ρx′(t−σ2)]−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.