Spatial pattern formation in a chemotaxis-diffusion-growth model

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Dynamics in a parabolic-elliptic chemotaxis system with growth source and nonlinear secretion (2019, methodology): “[13] for the particular case that θ = 2 and κ = 1.”
Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics (2016, background): “Numerical experiments suggest that despite possible absence of blow-up, such chemotaxis-growth systems may exhibit quite rich dynamics, including even chaotic behavior ([10], [17]).”
On the weakly competitive case in a two-species chemotaxis model (2016, result): “[37], emphasized by attractor results in [20, 32, 1, 33] or illustrated by recent results on transient growth phenomena in [51], [21].”
Emergence of large population densities despite logistic growth restrictions in fully parabolic chemotaxis systems (2017, background): “2) ([19]), as well as rich structures of associated steady-state sets in two-dimensional cases, including the occurrence of hexagonal patterns ([11]).”
A three-dimensional Keller–Segel–Navier–Stokes system with logistic source: Global weak solutions and asymptotic stabilization (2019, background): “2) according to numerical simulations ([21]) and analytical results on the associated set of equilibria ([32]), and since we do not expect the additional presence of a fluid interaction to have any regularizing effect in this regard, our exploration in this direction will concentrate on the case whe”