Spatio-temporal chaos in a chemotaxis model

By Kevin J. Painter, Thomas Hillen. 2011

222 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Molecular Biology, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/339fb33a17f6481e3af7fccfe929701ba777c26a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Modeling and Simulation

In Molecular Biology

In Public Health, Environmental and Occupational Health

Citations in the corpus

Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source (2014, background): “The richness of dynamics and pattern formation exhibited by chemotaxis models with growth [18, 10] however indicates that any speculation about asymptotical behaviour, especially about convergence to homogeneous states, should be backed by rigorous examinations.”
Blow-up in a higher-dimensional chemotaxis system despite logistic growth restriction (2011, background): “spatially one-dimensional case this problem seems to allow for chaotic behavior ([9]).”
Boundedness and global existence in the higher-dimensional parabolic–parabolic chemotaxis system with/without growth source (2015, background): “Recent numerical simulations indicate that even in 1-D this problem with g(u) = μu(1 − u) seems to allow for chaotic behavior [18].”
Emergence of large population densities despite logistic growth restrictions in fully parabolic chemotaxis systems (2017, background): “In presence of small values of μ when no such proliferation-dominated behavior can be expected, only little seems known beyond results on existence and dimension of exponential attractors in two-dimensional frameworks ([17], [16], [2]); after all, large-time extinction phemonena, as numerically obse”
Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type superlinear degradation (2018, background): “1), as revealed in numerical experiments and moreover indicated by formal analysis ([27], [22]).”
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].”
Blow-up prevention by quadratic degradation in a two-dimensional Keller–Segel–Navier–Stokes system (2016, result): “That this cannot be expected for general r > 0 and μ > 0 is indicated by the numerical experiments for the corresponding chemotaxis-only system presented in [26], revealing the possibility of quite colorful oscillatory dynamics even in the case N = 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]).”
Very weak global solutions to a parabolic–parabolic chemotaxis-system with logistic source (2016, background): “Additionally, in [18] the authors numerically explore the dynamics of a one-dimensional Keller-Segel model incorporating a logistic growth term and demonstrate the capacity of the model to self-organize into multiple cellular aggregations.”
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”
Global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening (2014, background): “for the cell density u = u(x, t) and the signal concentration v = v(x, t) in the physical domain Ω ⊂ Rn, under appropriate choices of the parameters d1, d2, χ, r, μ, α and τ ([12]).”