Gourley, Stephen A.; Ruan, Shigui Convergence and travelling fronts in functional differential equations with nonlocal terms: A competition model. (English) Zbl 1040.92045 SIAM J. Math. Anal. 35, No. 3, 806-822 (2003). Summary: We consider a two-species competition model described by a reaction-diffusion system with nonlocal delays. In the case of a general domain, we study the stability of the equilibria of the system by using the energy function method. When the domain is one-dimensional and infinite, by employing linear chain techniques and geometric singular perturbation theory, we investigate the existence of travelling front solutions of the system. Cited in 1 ReviewCited in 93 Documents MSC: 92D40 Ecology 35K57 Reaction-diffusion equations 92D25 Population dynamics (general) 35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions) Keywords:competition-diffusion; equilibrium; stability; travelling front; energy function; geometric singular perturbations PDFBibTeX XMLCite \textit{S. A. Gourley} and \textit{S. Ruan}, SIAM J. Math. Anal. 35, No. 3, 806--822 (2003; Zbl 1040.92045) Full Text: DOI