title: Competitive exclusion in a two-species chemotaxis model.
abstract: We consider a mathematical model for the spatio-temporal evolution of two biological species in a competitive situation. Besides diffusing, both species move toward higher concentrations of a chemical substance which is produced by themselves. The resulting system consists of two parabolic equations with Lotka-Volterra-type kinetic terms and chemotactic cross-diffusion, along with an elliptic equation describing the behavior of the chemical. We study the question in how far the phenomenon of competitive exclusion occurs in such a context. We identify parameter regimes for which indeed one of the species dies out asymptotically, whereas the other reaches its carrying capacity in the large time limit.
authors: Institut für Mathematik, Universität Paderborn, 33098 , Paderborn, Germany.
authors: C
authors: C
authors: Stinner
authors: J I
authors: JI
authors: Tello
authors: M
authors: M
authors: Winkler
mesh_terms: D018407:Bacterial Physiological Phenomena; D002633:Chemotaxis / Q000502:physiology*; D016014:Linear Models; D055641:Mathematical Concepts; D008954:Models, Biological; D017711:Nonlinear Dynamics
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