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. Key words: delay differential equations, delay reaction-diffusion equations, Nicholson’s blowflies equation, heteroclinic solution, traveling waves. 2000 AMS Mathematics Subject Classification: 34K25, 34K30, 35K57 ∗ Corresponding author. Fax:[phone]; Tel: [phone]. Preprint submitted to Elsevier Science 9 May 2006 

• Type: Journal
• Year: 2007
• Where: AMC
• Authors: Teresa Faria, Sergei Trofimchuk
• Keywords: AMC 2007, Heteroclinic Solution, Reaction-diffusion Equations, Scalar Delayed Reaction-diffusion