Non-linear Dynamics Commons^™

Traveling Wave Solutions For Two Species Competitive Chemotaxis Systems, T. B. Issa, R. B. Salako, W. Shen

Faculty Research, Scholarly, and Creative Activity

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 …