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Updated: May 11, 2026

Measurement of Cellular Chemotaxis with ECIS/Taxis
Published on: April 1, 2012
Competitive exclusion in a two-species chemotaxis model
C Stinner1, J I Tello, M Winkler
1Institut für Mathematik, Universität Paderborn, 33098 , Paderborn, Germany.
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.
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