We consider a chemotaxis system consisting of one parabolic equation and one ordinary differential equation in one space dimension with a logarithmic chemotactic sensitivity function and the exponential growth of dynamics for the chemical attractant. The structure of positive solutions is studied from the viewpoint of infinite-dimensional dynamical systems.
"Structure of Solutions to a Chemotaxis System in One Space Dimension." Methods Appl. Anal. 12 (3) 221 - 238, September 2005.