Stationary solutions of a volume-filling chemotaxis model with logistic growth and their stability (Q2910861)

The authors obtain conditions for the existence of stationary solutions of a volume-filling chemotaxis model with logistic term, under homogeneous Neumann boundary conditions. They also show that the same system without the chemotaxis term does not admit pattern formations. By using of the explicit formula for the stationary solutions, which is derived by asymptotic bifurcation analysis, the authors establish the stability criteria and find a selection mechanism of the principal wave modes for the stable stationary solution by estimating the leading term of the principal eigenvalue. The stability of bifurcations is also investigated. A necessary and sufficient condition for the stability of pattern solutions is studied for the case where the carrying capacity is one half. Numerical simulations are presented.