Traveling waves and their spectral instability in volume–filling chemotaxis model.

In this paper, I consider a volume-filling chemotaxis model with a small cell diffusion coefficient and chemotactic sensitivity. By the geometric singular perturbation theory together with the center-stable and center unstable manifolds, one gets the existence of a positive traveling wave connecting the two constant steady states (0 , 0) and (b , α b β) with a small wave speed ϵc. In addition, the traveling wave is monotone for b ≥ 1 and is not monotone for 0 < b < 1. Moreover, by the spectral analysis it shows that the above traveling wave is spectrally unstable in some exponentially weighted spaces. [ABSTRACT FROM AUTHOR]