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), alpha/beta u(c)) at chi = (chi) over bar (k) Moreover, for each k >= 1, we prove that each Gamma(k) can be extended into a global curve, and the projection of the bifurcation curve Gamma(k) onto the chi-axis contains ((chi) over bar (k), infinity).