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Traveling Waves and Their Spectral Instability in Volume–Filling Chemotaxis Model

SSRN, ISSN: 1556-5068
2023
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Article Description

In this paper, we 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 $(b,\frac{\alpha b}{\beta})$ with a small wave speed $\epsilon c$. In addition, the traveling wave is monotone for $b\geq 1$ and is not monotone for $0

Bibliographic Details

Qi Qiao

Elsevier BV

Multidisciplinary; Chemotaxis; traveling wave; spectral instability; geometric singular perturbation theory

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