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≥ …

Competitive exclusion in a two-species chemotaxis model

C Stinner, JI Tello, M Winkler - Journal of mathematical biology, 2014 - Springer
We consider a mathematical model for the spatio-temporal evolution of two biological
species in a competitive situation. Besides diffusing, both species move toward higher …

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 …

Global bifurcation and pattern formation for a reaction–diffusion predator–prey model with prey-taxis and double Beddington–DeAngelis functional responses

D Luo, Q Wang - Nonlinear Analysis: Real World Applications, 2022 - Elsevier
Of concern in this paper is to propose an accurate description for the global bifurcation
structure of the nonconstant steady states for a reaction–diffusion predator–prey model with …

Global bifurcation of solutions for a predator–prey model with prey‐taxis

X Wang, W Wang, G Zhang - Mathematical Methods in the …, 2015 - Wiley Online Library
We study pattern formations in a predator–prey model with prey‐taxis. It is proved that a
branch of nonconstant solutions can bifurcate from the positive equilibrium only when the …

Global bifurcation in a toxin producing phytoplankton–zooplankton system with prey-taxis

Y Peng, Y Li, T Zhang - Nonlinear Analysis: Real World Applications, 2021 - Elsevier
In this paper, we first study the stability of the positive constant equilibrium and Turing
instability induced by prey-taxis for phytoplankton–zooplankton system with prey-taxis. Then …

Stability and bifurcation in a predator–prey system with prey-taxis

H Qiu, S Guo, S Li - International Journal of Bifurcation and Chaos, 2020 - World Scientific
In this paper, we consider a generalized predator–prey system with prey-taxis under
Neumann boundary condition, that is, the predators can survive even in the absence of the …

[HTML][HTML] A positivity-preserving finite element method for chemotaxis problems in 3D

R Strehl, A Sokolov, D Kuzmin, D Horstmann… - Journal of Computational …, 2013 - Elsevier
We present an implicit finite element method for a class of chemotaxis models in three
spatial dimensions. The proposed algorithm is designed to maintain mass conservation and …

Stationary solutions of a volume-filling chemotaxis model with logistic growth and their stability

M Ma, C Ou, ZA Wang - SIAM Journal on Applied Mathematics, 2012 - SIAM
In this paper, we derive the conditions for the existence of stationary solutions (ie,
nonconstant steady states) of a volume-filling chemotaxis model with logistic growth over a …

Sharp condition for blow-up and global existence in a two species chemotactic Keller–Segel system in 2

E Espejo, K Vilches, C Conca - European Journal of Applied …, 2013 - cambridge.org
For the parabolic–elliptic Keller–Segel system in 2 it has been proved that if the initial mass
is less than 8π/χ, a global solution exists, and in case the initial mass is larger than 8π/χ …