Positive periodic solutions for neutral delay ratio-dependent predator‐prey model with Holling type III functional response

By using a continuation theorem based on coincidence degree theory, some new and interesting sufficient conditions are obtained for the existence of positive periodic solutions for neutral delay ratio‐dependent predator–prey model with Holling type III functional response $\left\{\begin{array}{c}{x}^{\prime }(t)=x(t)[r(t)-a(t)x(t-{\sigma }_1)-\rho x^{\prime }(t-{\sigma }_2)]-\frac{c(t)x^2(t)}{m^2{y}^2(t)+x^2(t)}y(t)\text{,}\hfill \\ y^{\prime }(t)=y(t)\left[-d(t)+\frac{h(t)x^2(t-\tau (t))}{m^2{y}^2(t-\tau (t))+x^2(t-\tau (t))}\right]\text{.}\hfill \end{array}\right.$ An example is represented to illustrate the feasibility of our main results.