title: Diffusion, cross-diffusion and competitive interaction.
abstract: The cross-diffusion competition systems were introduced by Shigesada et al. [J. Theor. Biol. 79, 83-99 (1979)] to describe the population pressure by other species. In this paper, introducing the densities of the active individuals and the less active ones, we show that the cross-diffusion competition system can be approximated by the reaction-diffusion system which only includes the linear diffusion. The linearized stability around the constant equilibrium solution is also studied, which implies that the cross-diffusion induced instability can be regarded as Turing's instability of the corresponding reaction-diffusion system.
authors.affiliation: Department of Mathematics, Faculty of Humanities and Social Sciences, Iwate University, Morioka, 020-8550, Japan.
authors.forename: Masato
authors.initials: M
authors.lastname: Iida
authors.forename: Masayasu
authors.initials: M
authors.lastname: Mimura
authors.forename: Hirokazu
authors.initials: H
authors.lastname: Ninomiya
mesh_terms: D000465:Algorithms; D000818:Animals; D017753:Ecosystem; D008954:Models, Biological; D011156:Population Density; D011157:Population Dynamics; D011158:Population Growth