In this paper, we consider two species chemotaxis systems with Lotka–Volterra competition reaction terms. Under appropriate conditions on the parameters in such a system, we establish the existence of traveling wave solutions of the system connecting two spatially homogeneous equilibrium solutions with wave speed greater than some critical number c∗. We also show the non-existence of such traveling waves with speed less than some critical number c∗0 , which is independent of the chemotaxis. Moreover, under suitable hypotheses on the coefficients of the reaction terms, we obtain explicit range for the chemotaxis sensitivity coefficients ensuring c∗ = c∗0 , which implies that the minimum wave speed exists and is not affected by the chemoattractant.
Chemotaxis-models, Competition system, Traveling waves
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Mathematics and Statistics
T. B. Issa, R. B. Salako, and W. Shen. "Traveling wave solutions for two species competitive chemotaxis systems" Nonlinear Analysis (2021). https://doi.org/10.1016/j.na.2021.112480