A local excess of cells produces extra attractant. The resulting concentration gradient drives <chemotaxis> toward that excess, which further raises cell density and attractant production. This positive feedback causes aggregation when $\chi$ is large enough. Cell and chemical diffusion suppress short wavelengths, while death and chemical degradation suppress very long and homogeneous perturbations. Their competition selects the finite $k_c$, producing a <chemotactic pattern-forming instability> even though the homogeneous kinetic system is stable.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 355 / 2 / c / Solution

A chemotactic pattern-forming instability occurs when cells produce an attractant and drift up its gradient strongly enough that positive aggregation feedback overcomes diffusion and turnover at a finite wavelength.


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 Incoming links: Chemotactic pattern-forming instability