Dynamics and diffusion limit of traveling waves in a two-species chemotactic model with logarithmic sensitivity

Abstract

This paper discusses the traveling wave analysis of the two-species chemotaxis model with logarithmic sensitivity, which describes diverse biological phenomena such as the initiation of angiogenesis using reinforced random walks theory and the chemotactic response of two interacting species to a chemical stimulus. The objectives are to quantitatively establish the existence of traveling wave solutions only for the parameters in certain parameter regimes. Moreover, we incorporate recent results and discuss many other aspects of traveling wave solutions such as asymptotic decay rates and convergence as the chemical diffusion coefficient goes to zero. The main techniques are analyzed and the analytical results are reviewed graphically.