Global Bifurcation of Stationary Solutions for a Volume-Filling Chemotaxis Model with Logistic Growth.

In this paper, we show how the global bifurcation theory for nonlinear Fredholm operators (Theorem 4.3 of [Shi & Wang, 2009]) and for compact operators (Theorem 1.3 of [Rabinowitz, 1971]) can be used in the study of the nonconstant stationary solutions for a volume-filling chemotaxis model with logistic growth under Neumann boundary conditions. Our results show that infinitely many local branches of nonconstant solutions bifurcate from the positive constant solution (u c , α β u c) at χ = χ ¯ k . Moreover, for each k ≥ 1 , we prove that each Γ k can be extended into a global curve, and the projection of the bifurcation curve Γ k onto the χ -axis contains ( χ ¯ k , ∞). [ABSTRACT FROM AUTHOR]