Competing effects of attraction vs. repulsion in chemotaxis

Y Tao, ZA Wang - Mathematical Models and Methods in Applied …, 2013 - World Scientific
We consider the attraction–repulsion chemotaxis system under homogeneous Neumann
boundary conditions in a bounded domain Ω⊂ ℝn with smooth boundary, where χ≥ 0, ξ≥ …

Generalizing the Keller–Segel model: Lyapunov functionals, steady state analysis, and blow-up results for multi-species chemotaxis models in the presence of …

D Horstmann - Journal of nonlinear science, 2011 - Springer
In this paper we extend the famous Keller–Segel model for the chemotactic movement of
motile species to some multi-species chemotaxis equations. The presented multi-species …

[HTML][HTML] Asymptotic stability of a two species chemotaxis system with non-diffusive chemoattractant

M Negreanu, JI Tello - Journal of Differential Equations, 2015 - Elsevier
We study the behavior of two biological populations “u” and “v” attracted by the same
chemical substance whose behavior is described in terms of second order parabolic …

Remarks on the blowup and global existence for a two species chemotactic Keller–Segel system in 2

C Conca, E Espejo, K Vilches - European Journal of Applied …, 2011 - cambridge.org
For the Keller–Segel model, it was conjectured by Childress and Percus (1984, Chemotactic
collapse in two dimensions. In Lecture Notes in Biomath. Vol. 55, Springer, Berlin …

Simultaneous finite time blow-up in a two-species model for chemotaxis

EE Espejo, A Stevens, JJL Velázquez - 2009 - degruyter.com
A system of two classical chemotaxis equations, coupled with an elliptic equation for an
attractive chemical, is analyzed. Depending on the parameter values for the three respective …

On a two species chemotaxis model with slow chemical diffusion

M Negreanu, JI Tello - SIAM Journal on Mathematical Analysis, 2014 - SIAM
In this paper we consider a system of three parabolic equations modeling the behavior of
two biological species moving attracted by a chemical factor. The chemical substance …

[HTML][HTML] Boundedness and asymptotic stability of solutions to a two-species chemotaxis system with consumption of chemoattractant

L Wang, C Mu, X Hu, P Zheng - Journal of Differential Equations, 2018 - Elsevier
This paper deals with a two-competing-species chemotaxis system with consumption of
chemoattractant {ut= d 1 Δ u−∇⋅(u χ 1 (w)∇ w)+ μ 1 u (1− u− a 1 v), x∈ Ω, t> 0, vt= d 2 Δ …

Spiky and transition layer steady states of chemotaxis systems via global bifurcation and Helly's compactness theorem

X Wang, Q Xu - Journal of mathematical biology, 2013 - Springer
The most important phenomenon in chemotaxis is cell aggregation. To model this
phenomenon we use spiky or transition layer (step-function-like) steady states. In the case of …

Convergence of global and bounded solutions of a two-species chemotaxis model with a logistic source.

K Lin, C Mu - … & Continuous Dynamical Systems-Series B, 2017 - search.ebscohost.com
In this paper, we consider a system of three parabolic equations in high-dimensional
smoothly bounded domain... which describes the mutual competition between two …

High-order positivity-preserving hybrid finite-volume-finite-difference methods for chemotaxis systems

A Chertock, Y Epshteyn, H Hu, A Kurganov - Advances in Computational …, 2018 - Springer
Chemotaxis refers to mechanisms by which cellular motion occurs in response to an
external stimulus, usually a chemical one. Chemotaxis phenomenon plays an important role …