LAUSR

This paper is concerned with the steady state problem of a chemotaxis model with singular sensitivity function in a one dimensional spatial domain. Using the chemotactic coefficient $$\chi $$χ as the bifurcation parameter, we perform local and global bifurcation analysis for the model. It is shown that positive monotone steady states exist as long as $$\chi $$χ is larger than the first bifurcation value $$\bar{\chi }_1.$$χ¯1. We further obtain asymptotic profiles of these steady states, as $$\chi $$χ becomes large. In particular, our results show that the cell density function forms a spike, which models the important physical phenomenon of cell aggregation.