Positive heteroclinics and traveling waves for scalar population models with a single delay

The existence of positive heteroclinic solutions is proven for a class of scalar population models with one discrete delay. Traveling wave solutions for scalar delayed reaction-diffusion equations are also obtained, as perturbations of heteroclinic solutions of the associated equation without diffusion. As an illustration, the results are applied to the Nicholson’s blowflies equation with diffusion ∂N ∂t (t, x) = d 2N ∂x2 (t, x)− δN(t, x)+ pN(t− τ, x)e−aN(t−τ,x) in the case of p/δ > e, for which the nonlinearity is non-monotone.