Traveling Wave Solutions for Two Species Competitive Chemotaxis Systems
Nonlinear Analysis: Theory, Methods and Applications
First page number:
Last page number:
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 c0∗, 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∗=c0∗, which implies that the minimum wave speed exists and is not affected by the chemoattractant.
Chemotaxis-models; Competition system; Traveling waves
Applied Mathematics | Biostatistics
Traveling Wave Solutions for Two Species Competitive Chemotaxis Systems.
Nonlinear Analysis: Theory, Methods and Applications, 212