Travelling front solutions arising in the chemotaxis-growth model

Abstract

We consider a bistable reaction-diffusion-advection system describing the growth of biological individuals which move by diffusion and chemotaxis. We use the singular limit procedure to study the dynamics of growth patterns arising in this system. It is shown that travelling front solutions are transversally stable when the chemotactic effect is weak and, when it becomes stronger, they are destabilized. Numerical simulations reveal that the destabilized solution evolves into complex patterns with dynamic network-like structures.

A model aided understanding of spot pattern formation in chemotactic E. coli colonies

“…We remark that the choice of χ(c) has been found to significantly affect the formation of patterns (see Schaaf [20] and Funaki et al [8] and the references there in). This system is a simplified model of slime mold aggregation in species such as Dictyostelium discoideum [13], which describes the coupled behaviour of an amoeba population diffusing and moving up gradients of a chemical which the amoeba excrete themselves.…”

Absence of collapse in a parabolic chemotaxis system with signal‐dependent sensitivity

“…Such a blow-up is evidently connected to the phenomenon of cell aggregation. Therefore, its occurrence is frequently employed to justify the biological relevance of a suggested model, although in the recent years many results concerning pattern formation of bounded solutions have illustrated a rich dynamical structure also of some of those versions of (1.1) for which no collapse happens (see [5,7,17,[24][25][26]30], and the discussion in [11, Sect. 6.1.2]).…”

Anomalous invasion in a 2d model of chemotactic predation

“…(2a) above [7][8][9]. In some cases these are present because the aim of the investigation is to study properties of general diffusion-reaction systems, which can include purely chemical reactions.…”