Wavefront invasion for a volume-filling chemotaxis model with logistic growth

This paper is devoted to study the propagation of the pattern in a large domain for a volume-filling model with chemotaxis. By deriving the real Ginzburg–Landau equation governing the evolution of pattern amplitude we show that the pattern invades the whole domain in the form of a traveling wave, which implies the existence of a traveling front solution connecting a uniform steady state and a stationary pattern in the considered model with a large chemotactic parameter. The numerical results are in good agreement with the theoretical results. This work is a significant supplement of the related literature.