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.