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arXiv · 2010.11335

Traveling wave solutions for two species competitive chemotaxis systems

T. B. Issa·R. B Salako·W. Shen
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Abstract

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.

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T. B. Issa, R. B Salako, W. Shen. 2020-10-21. Traveling wave solutions for two species competitive chemotaxis systems. https://arxiv.org/abs/2010.11335

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