Competitive exclusion in a two-species chemotaxis model
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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.
KeywordsChemotaxis Stability of solutions Asymptotic behavior Competitive exclusion
Mathematics Subject Classification (2010)92C17 35K55 35B35 35B40
The second author is partially supported by Ministerio de Economía y Competitividad under grant MTM2009-13655 (Spain) and CCG07-UPM/000-3199 at UPM.
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